Physics 104 Exam 2
Current, Voltage, and Power -Three different resistors are connected to a voltage source as shown. What is the correct ranking of power dissipated by each resistor? +explain?
-A) P A > P B > PC +since the resistors are all in parallel -> the ∆V's are the same in all the resistors -> and thus only the resistance differences between the resistors matters! (larger resistance -> smaller power) -> in pic! +really just rearranging the power equation with ohms law and what not!
lecture 6b -Before an MRI scan is performed on a patient, the room must be cleared of all metallic objects. Why? -MRI ideas?
-B) MRI machines produce strong magnetic fields that can attract some metallic objects -> stuff could be pulled from around the room! -MRI +really just a giant solenoid -> usually a 3T B-field +3T B-field -> about 10,000x the B field of earth (which is used for compass needle)
Magnetic Flux -This is a side view of three square loops in uniform magnetic fields. Through which loop is the magnetic flux the largest? +explain
-C) Loop C +calculate each with equation! +use the correct ø !!
Circular motion in magnetic fields -What is the direction of the particle's acceleration at this later instant? +explain?
-D) down +B force exists (B field is perpendicular to the velocity) and thus an accelaration must exist (F=ma, Netwons 2nd law!) and acceleration is in same direction as force!
Waves & Energy -Electromagnetic waves transport? -Rate of energy transfer is? -intensity? +idea flow? +area of shells? -Erms and Brms?
-Electromagnetic waves transport energy as they propagate -Rate of energy transfer is related to the square of the amplitude -intensity is power/area +power emitted from source is constant but is spread out over a 3D area -> area is generally 4(pi)r^2 because its the area of a sphere +in pic -in pic!
Kirchhoff's Rules -2 rules and main ideas with each? -importance?
-Loop Rule: ΔVloop = 0 for a complete loop around a circuit (that is, you end where you begin). Between two different points, ΔV A->B = VB - VA . The loop rule is a statement about the conservation of energy. -Junction Rule: ∑ i,in = ∑i, out at every junction. Note that, most of the time, you will need to determine the direction of currents, and thus what qualifies as in and out. If you find a negative current, this just means you chose the wrong direction (just pick one and test it out and change it if you have to!) The junction rule is a statement about the conservation of charge. (can destroy or create charge...) -these are really important -> use these! especially when stuck on problems!!
Series -Two circuit components are in series if you can?. +have same what? +where does i change? +ex?
-Two circuit components are in series if you can trace a path from the end of one to the beginning of the other without passing through a junction. +have same i's +i changes at junctions +ex in pic
A Loop's B-Field -questions in pic?
-all point out of the page! (loop could be any shape really...? circle or square for sure...) +Use RHR-2 or RHR-3 to solve this (RHR-3 would be faster!)
Current events -learning for today?
-in pic
Lecture 5b -getting help in physics?
-in pic
Review: magnetism -main ideas and equations?
-in pic
Review: magnetic force -In what direction is the force on the current-carrying wire?
-in pic +RHR-1
review: Electromagnetic Induction -A conducting loop moves into a uniform magnetic field from left to right as shown. What is the direction of induced current at each instant shown?
-in pic +magnetic flux is not changing in the middle and thus no current is induced +magnetic flux increases as the ring moves into the loop and thus current is induced +magnetic flux decreases as the ring moves out of the loop and thus current is induced
The Solar spectrum -intensity of solar radiation felt by earth from sun?
-in pic (about 1.3 kW / m^2) +lots of infrared! +Y-axis is intensity / wavelength
Flux and flashlights -The current induced in the wire coil is?
-in pic! -Current directions would reverse after the magnet moves through the coil.
Resistance and gradients -What can we do to increase the current through the segment of wire? -graphs?
-think Ohm's law -> in pic +increase ∆V or decrease R to increase i -in pic ??
Question: Your iclicker operates at a frequency of approximately 900 MHz ( 900 x 106 Hz ). What is the approximate wavelength of the EM wave produced by your iclicker?
0.3m Use equation!
Resistors and "hallways" (in pic) Which resistor will have the greater resistance 𝑅?
A) Resistor 1 -equations -> in pic!
Lecture 5a Thinking about Current Which of the following best describes what happens if you touch a live power line?
Charges in your body start to move through the potential difference between the wire and the ground
Current? todays agenda
Current: Charges in motion moving charges and circuits -> in pic!
Measure the speed of light at home
in pic
More Circuit Training
in pic
chapter summary
in pic (ignore 23.4!!)
bridgeset The figure shows a mass spectrometer in which negative ions that have passed through a velocity selector enter a region of uniform magnetic field. Which of the following changes will decrease the distance 𝑑d where the ions land after they have been deflected by the external magnetic field 𝐵⃗ B→?
Bridgesets -> lots of right hand rule (rhr)! Look at one mistake below! decreasing the voltage across the plates of the velocity selector. decreasing the strength of the magnetic field 𝐵⃗ 0B→0 in the velocity selector flipping the direction of the magnetic field by 180∘180∘ in the region the ions enter after they leave the velocity selector decreasing the voltage across the plates of the velocity selector. The radius r of the semicircular trajectory of the ion in the external field region is given by the expression 𝑟=𝑚𝑣/𝑞𝐵 where 𝑚m (units always put mm instead of m when copied for some reason!) is the mass of the ion, 𝑣v is the velocity of the ion, 𝑞q is the charge on the ion, and 𝐵B is the magnitude of the external field. Express this relation in terms of the diameter 𝑑d . 𝑑=2𝑚𝑣/𝑞𝐵 Assuming the charge and mass of the ion are fixed, you can reduce the diameter by decreasing the velocity of the particle or by increasing the strength of the external field. Increasing the field strength is not an option, so one of the options must result in a decreased ion velocity. Examine the equilibrium of the electric and magnetic forces in the velocity selector. 𝑞𝐸0=𝑞𝑣𝐵0 Cancel the common charge and solve for v . 𝑣=𝐸0𝐵0 From this expression, note that decreasing 𝐸0E0 or increasing 𝐵0B0 will decrease the velocity chosen by the selector. Increasing 𝐵0B0 is not an option, but decreasing 𝐸0E0 is an option through reducing the voltage across the plates of the selector. Finally, note that flipping the direction of the external field will only flip the curvature of the trajectory in the field region; it will not alter the diameter of the semicircle. equation relating E field to B field??
Circular motion in magnetic fields -What is happening to the speed of the particle during this motion? +explain? -situation in pic? +when does this occur? -r of the circle equation?
C) Speed is constant +acceleration is present only because the velocity is constant changing direction, but speed itself is not increasing or decreasing! -uniform circular motion! +occurs when the v of the charged particle is perfectly perpendicular to the B field -in pic +can you use this in spiral case (next slides...)??
Four electrons, A, B, C, and D, are fired into a region that has a uniform magnetic field pointing into the screen. The initial speeds of the electrons are equal, and their velocity vectors are indicated by red arrows in the figure. Each electron will follow a trajectory that is bent by the magnetic force. (in pic) For which electrons is it possible for the magnetic force to bend the trajectory such that the electron exits the field at the point where the proton enters the field?
Answer: electron A and C +use right hand rule to solve! + Apply the right-hand rule for moving charges in a magnetic field to determine that only electrons A and C could potentially reach the proton's entry point.Point the fingers of your right hand downward in the direction of Electron A's velocity, curl your fingers inward toward the screen in the direction of the magnetic field, and note that your thumb points to the right. Since the electron charge is negative, flip your hand over so your thumb points to the left. The magnetic force will cause electron A's trajectory to bend toward the proton edge, so it could exit the field at the proton's entry point. The same procedure shows that electron C could also exit the field at the proton's entry point, though the magnetic field would need to be weaker. Apply the right-hand rule to electron B to discover that its trajectory will bend away from the proton's entry point, and to electron D to discover that its trajectory will bend toward the right edge.
Quiz 6 mistake...
Be careful when determining the direction of the B field -consider the 4 different B field tangent vectors on top, bottom, left, and right from the wire when determining direction of the B field from a long current carrying like in pic (always consider these if it will help, even if its not a long current carrying wire...) +ex: wire on left in pic would have a B field vector above it that is pointing exactly to the right +ex: wire on the right would have a B field vector to the left of it that is pointing directly down! -in pic! -use RHR-1 to find the direction of the net force once you know that that direction of the B field on the top shaded wire is down +wire on left gives a B field that is down to the right (on top shaded wire) +wire on right gives a B field that is down to the left (on top shaded wire) +left and right B field components cancel (on top shaded wire) (Same magnitudes and what not) +B field is directly down (on top shaded wire) +RHR-1 tells us the B force would then be pointing to the right on the top shaded wire!
looking at voltage to determine if in parallel?
"think" current going in both forward and reverse idea! (dont make mistake of thinking ∆V after resistors in parallel are different) -> their ∆V is the same! ?? -logic through it! ....??
resistance force (Fr) Suppose we drop two spheres, one in a cylinder of glycerol, a very viscous liquid, and one in a cylinder of water, a much less viscous liquid. The spheres have the same diameters and masses masses. What will happen?
) The sphere in glycerol takes longer to reach the bottom. +explained on previous slide
Capacitor charging basics -Suppose and ε = battery 8 V, R in = 4 Ω, and C = 0.15 F series. Suppose we flip switch s and complete the circuit. +What is the maximum current that will flow? explain? -flow of closing switch to charge capacitor?
+E) ε /R -> use equations! +B) t=∞ -> use equations! -switch closed -> charged builds up on the capacitor -> + part of capacitor repels incoming current (Qmax occurs and i stops) +as t increases with charging capacitor in series -> i decreases and q increases
Question: The north pole of one magnet attracts the south pole of another magnet. The needle of a compass is itself a magnet; the end of the needle that points north is capped with an arrow and often painted red. In light of this, explain why the arrow‑capped end of a compass needle is attracted to the North Pole of the Earth.
- answer: The geographic North Pole is actually the south magnetic pole of the Earth. + If you imagine the Earth as a giant bar magnet, the south end of the magnet is near the geographic North Pole of the Earth. Geographic north and true magnetic north are not the same thing.
Question: A circular wire loop is located inside a region of space containing a magnetic field, as shown. The direction of the magnetic field is out of the screen, parallel to the axis of the loop, and the magnitude of the magnetic field increases as a function of time. -What is the direction of the induced current in the loop?
- clockwise +explanation in next slide pic!
Electromagnetic Induction -A change in magnetic flux through a loop creates an? +The magnitude depends on? +flow? +induced emf acts like? -Faradays law? -How can we change Φ?
-A change in magnetic flux through a loop creates an induced emf around the loop. +The magnitude depends on the rate of change. +change magnetic flux -> induce emf -> E field generated (by emf) -> induced current -> induced B field (in direction that opposes the original change in magnetic flux) +induced emf acts like a battery (causes i to flow by generated an electric field).... like a voltage! -in pic -How can we change Φ? +change A -> stretch/squash loop +change B -> change B field strength +change ø -> rotate loop!
Current, Voltage, and Power -A 60-Watt light bulb is connected to a 120 V power supply. What equation would you use to find the current through the lightbulb? +explain? -What is the current through the bulb? +explain?
-A) P=iV +easiest equation to use here! +P is power dissipated by the resistor, i is current flowing through the resistor, and ∆V is voltage drop ax the resistor +dissipated energy per unit time is power -> in pic! -A) 0.5 A +plug numbers into above equation!
Forces between parallel wires -What will happen to two parallel wires with current running in the same direction? +explain? -currents in same direction vs opposite directions?
-A) The wires will attract each other -> in pic! +find the direction of the B field of current 1 at location of current 2 -> use RHR-1 to determine if B force (from current 1 at current 2) is pointing toward or away from current 1 -> pointing towards (attractive) and pointing away (repel) +repeat process to find B force of current 2 on 1 to verify you are right! (should give the same result) -in pic -long straight currents in same direction -> attract each other -long straight currents in opposite directions -> repel each other
Electrons in a B-field -A beam of electrons travels from left to right in this evacuated tube. The S pole of a bar magnet is brought close to the side of the beam. In which direction is the beam deflected? +explain?
-A) Up (↑) +B field of the magnet is coming out toward us +v of the electrons is to the right +use RHR-1 to find direction of particle -> remember to flip direction bc this is a - electron! +answer would be down if we flipped the magnetic
lecture 7a -Faraday flashlight; This emergency flashlight does not require batteries. After you shake the flashlight, an LED bulb can be switched on for a few minutes. How does this work? +flow?
-A. Shaking the flashlight moves a magnet back and forth through a wire coil, which induces a current and charges a capacitor. +change magnetic flux -> induce emf -> E field generated -> induce current -> charge capacitor (which powers the battery!)
Changes with time -As you saw in the prelecture, adding a capacitor to a circuit adds a new dimension to our analysis? +attribute of the circuit? -lets take a closer look at? -ideas with series charging circuit?
-As you saw in the prelecture, adding a capacitor to a circuit adds a new dimension to our analysis - change in time! +attribute of the circuit, such as current or voltage differences are no longer constant -lets take a closer look at a circuit with a capacitor, resistor, and battery in series -ideas with series charging circuit +at t = about 0 -> i is max and q is 0 +at t = infinity -> i is 0 and q is max
Just can't resist -You saw this circuit in the prelecture: What will the charge on the capacitor be a long time after switch S is closed? +Explain? -current flowing into capacitor idea?
-B -> C 𝛆1 +reason using the q= C∆V equation (and ideas about loops in circuit!) -> capacitor has a voltage drop and at max the voltage drop must be the same as that of the battery... (in parallel...) +also consider using equations.... -> mainly for in series, can be used at instances in parallel... -current flows into top of capacitor and out of bottom of capacitor but doesn't flow through it!
Drift speed -A 1 A current is flowing through a copper wire with a circular cross-section. If the wire has a radius of 0.5 mm and contains 8.5 x 10 28 charge carriers per m3 , how far will a charge carrier travel in 1 hour? -SI unit time?
-B) 0.33 m +in pic -SI unit time = seconds!
Series or parallel -In which case will the bulbs be brighter (more/larger current -> more brightness)? +explain? -series and parallel with ∆V and i? -removing bulb?
-B) When they're connected in parallel +in series -> ∆V will be split bw all bulbs (larger ∆V in parallel -> larger current!) +in pic! -parallel i is different bw resistors ∆V is constant bw resistors in pic! -series i is same bw resistors ∆V is different bw resistors in pic! -removing bulb from series -> all bulbs go out +need a (fully connected) loop for the current to travel! -removing bulb from parallel -> other bulbs stay on!
Circular motion in magnetic fields -What is the direction of force on the positively charged particle? +explain? -coming in and out of page notation?
-B) left +use RHR-1 -C in pic -> coming out of page (tip of arrow coming at you) -D in pic -> going into page (end of arrow going away from you)
Current context -You apply a uniform electric field to three materials: a solid conductor, a solid insulator, and a fluid with positive and negative ions. Assuming the total charge in all the materials is the same, in which will you create the largest current?
-C) Fluid with ions +2 currents occur in the water -> 1 from + charges moving and other from - charges moving -> combine to make 1 larger current +in liquids -> + and - cahrges can move +in solids -> only - electrons can really move (+ charges are locked in place in solids for most part) +no current in the insulator bc the - charges cant move +conductor has half the current of fluids?? bc - q's can move but +q's cant move?? +in pic
Force on a current-carrying wire -A copper rod is positioned in a uniform magnetic field. Current flows through the rod in the direction shown. In which direction is the force on the rod? +explain? +flipping current? -B force on current equation? +variables?
-C) Left +use RHR-1 (think of i and v tho!) +flipping current -> flips direction of B force -in pic +i is current +l is length of wire +B is magnitude of B field +sinø -> ø is angle bw current and B field; again only component of the i perpendicular to the B field matters (sinø is just used in eqs to find this perpendicular component!) +if i is parallel (or antiparallel) to the B field -> ø is 0 and B force is 0
Lecture 6a -In proton therapy, beams of protons are used to irradiate and destroy tumors. How are magnetic fields important in the use of proton therapy? +explain?
-C) The paths of protons are controlled using forces from magnetic fields. +magnetic fields (B fields) can be used to make protons move in circular path
Earth's Magnetic Field -Charged particles moving in loops are likely responsible for? +explain? -Do some research on the "Dynamo Theory" if you're interested. -earth N and S geographic poles
-Charged particles moving in loops are likely responsible for the Earth's magnetic field. +current (i) in earth (molten inner fluid of earth has charged particles flowing through it) -> flows in loops and thus makes a B field -Do some research on the "Dynamo Theory" if you're interested. -earth +geographic N pole -> actual S magnetic pole of earth +geographic S pole -> actual N magnetic pole of earth
Three different series 𝑅𝐶RC circuits are built. Each circuit is connected to an identical power supply that delivers a voltage 𝜀ε . The circuits use identical capacitors but different resistors. The charging process of each capacitor is recorded and plotted, as shown. -> in pic! Which circuit has the resistor with the greatest resistance?
Circuit 3 -manipulate variables in equation and be careful with - exponents! -larger RC (time constant) -> slower rate of change (Smaller slope) -smaller RC (time constant) -> faster rate of change (large slope)
Question: in pic Suppose that part of a wire in a circuit is only half the diameter of the rest of the wire. Compared to the rest of the wire, the current in the thinner part is
-Compared to the rest of the wire, the current in the thinner part is -the same -> Current is the amount of charge moving past any point in the circuit per unit of time. Much like fluid flowing in a pipe, the amount of charge moving through the circuit is constant. Moving charges do not "pile up" or accumulate at any point in the circuit because electrostatic forces ensure that current remains constant throughout the wire in the steady state. Nor can charges be added or removed from the flow of charge since the circuit is a closed system. Therefore, the value of the current is the same everywhere in the circuit. +this is talking about current flowing through a wire that is made more thin -> is not referencing a resistor -ask about!!
Earth's radiation budget -Earth both?
-Earth both absorbs and emits EM radiation. It absorbs incoming radiation from the Sun (sunlight) and radiates EM waves back into space.
Electromagnetic Waves -Electromagnetic waves consist of? -generating an E field in an em wave? -generating a B field in an em wave? -what does ac generator do? -demo? -speed of light? ....remember that?
-Electromagnetic waves consist of oscillating electric & magnetic fields -generating an E field in an em wave +AC generator drives current to flow back in forth in a wire -> E-field is ultimately driving the current to go back and forth in the wire -> E field leaks out (sent into space) of the wire as a wave that is parallel to the wire +E field is reinforced by changing B field -generating a B field in an em wave +AC generator creates a current in a long straight wire -> B-field forms around the wire and is sent into space-> B field is perpendicular to both the wire and the E-field +B field is reinforced by changing E field -AC generator -> drives current back and forth in the wire +makes E field (parallel to wire) and B field (perpendicular to wire) that reinforce each other +E and B field are perpendicular to each other! -demo +lightbulb should light up if device (lightbulb with long metal antennas attached to either side) is held by AC generator if the receiving antenna is parallel to the AC generator wire (E field is parallel to the wire with the ac generator -> drives current is parallel to the antenna.... DOES NOT drive current if perpendicular) +E filed from wire and AC generator must align with the metal antenna (parallel) to induce a current in the metal antennas and make the lightbulb turn on -all EM waves -> travel at the same speed of light; 3E8 +but EM waves differ in the frequencies and wavelengths! ..... remember that B and E fields propagate through space when they are created....??
Electromagnetic Waves -Electromagnetic waves consist of? -shown graphs are usually? +why? -important equation? -Hz? -planes of E and B field?
-Electromagnetic waves consist of oscillating electric & magnetic fields -shown graphs are usually deceiving +E and B fields actually fill up volume (fill up space) -in pic +Eo is E field amplitude (peak E field) +Bo is B field amplitude (peak B field) +c is speed of light +thus we see that B field amplitude is much smaller than E field amplitude... in EM waves -Hz -> SI unit of frequency -> 1/second -E field is in one plane (parallel to wire and AC generator) +B field is in different plane (perpendicular to wire and AC generator)
B-field of a current loop -Magnetic fields can also be produced by? -the B field direction? -the B field loops? -the B field vectors?
-Magnetic fields can also be produced by current loops (in pic) -the B field direction +N -> S poles outside of manget +S -> N pole inside of magnet +in pic! -B field -> forms full loops (do not terminate!) +E fields terminate at - charges (start at + charges...) -B field vectors -> like tangent to the B field lines +see last slide -> important!
22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field -Magnetic fields exert a force on a? -The direction of the force on a moving charge is given by? +The force is?
-Magnetic fields exert a force on a moving charge q, the magnitude of which is 𝐹=𝑞𝑣𝐵sin𝜃, -The direction of the force on a moving charge is given by right hand rule 1 (RHR-1): Point the fingers of the right hand in the direction of 𝑣, the palm in the direction of 𝐵, and the thumb points in the direction of 𝐹 +The force is perpendicular to the plane formed by 𝐯 and 𝐁. Since the force is zero if 𝐯 is parallel to 𝐁, charged particles often follow magnetic field lines rather than cross them.
22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications -Magnetic force can supply centripetal force and cause a charged particle to move in a?
-Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius 𝑟=𝑚𝑣/𝑞𝐵 where 𝑣 is the component of the velocity perpendicular to 𝐵 for a charged particle with mass 𝑚 and charge 𝑞 +if velocity is parallel to B field -> not circular force +if velocity is perpendicular to B field -> only circular force + if is bw perpendicular and parallel to B field -> experiences some circular force and moves forward?? + r is the RADIUS of the circular that the charged particle travels in! -> keep in mind that for mass spectrometer, r still gives the radius (of the semicircle in case of mass spec) -> must use 2r to find the distance that the electron would land from the spot it was shot out! -> discussion problem in 6a!!
unit 2 overall questions -does resistance change if ∆V or i changes? -is resistor or capacitor closer to the emf source in an RC circuit? -Vd and direction compared to i? -best reception for picking up EM waves? -amplitudes of E and B fields compared to each other in an EM wave? -amplitudes of E and B fields (like in EM wave) with distance?
-NO -> resistance only depends on pL/A (relate to idea of capacitance not changing if q or ∆V changing...) -doesnt matter! same analysis either way! -Vd of + charges flowing is same direction as i +but the Vd of the actual electrons is opposite direction as i -orient the receiving antenna parallel to the E field coming from the sending antenna (also is perpendicular to the incoming B field then!) -amplitudes relate in equation E = cB +c is speed of light +E is E field amplitude +B is B field amplitude -amplitudes of E and B fields (like in EM wave) -> decrease with increasing distance! +wavelength and frequency remain constant over distance tho (and thus speed remains constant too...)
Current and direction -Remember, by convention, we define current as the? -In a segment of a tube containing + and ions in a fluid, a total of +3 C of charge moves through to the right and -3 C of charge moves through to the left over a period of 30s. What is the current in the tube?
-Remember, by convention, we define current as the flow of positive charge. -A) 0.2 A to the right +both + moving to right and - moving to left make a + current (explained earlier) and thus currents add! -> in pic
Two magnetic Fields! -The fact that current must be flowing through the wire loop for the motor to work means that the loop is? -That is, in all the pictures of loops in fields you've seen so far, there are really? -We can understand how current loops respond to external magnetic fields by? So let's explore the B-field that a current in a loop creates... -current creates?
-The fact that current must be flowing through the wire loop for the motor to work means that the loop is generating its own B-field. -That is, in all the pictures of loops in fields you've seen so far, there are really two fields - the one created by the current in the loop and the one created by an external source (such as a magnet) -We can understand how current loops respond to external magnetic fields by imagining two magnets interacting. -So let's explore the B-field that a current in a loop creates... -B fields!
Lenz's Law -The induced current will create a magnetic field that? +flow? +draw out what to help?
-The induced current will create a magnetic field that opposes the change in the magnetic flux +change magnetic flux -> induce emf -> E field generated (by emf) -> induced current -> induced B field (in direction that opposes the original change in magnetic flux) +Draw out the Bext (external) and the Bind (induced)
Magnetic field created by currents -Right hand rule #2: for B field due to a current? -equation for B field created by long straight current carrying wire? -consider? -units of B field?
-To find the direction of the B-field of a long straight current-carrying wire, line your right thumb with the direction of the current and your fingers will curl in the direction of B. -in pic +r = distance from center of wire +mew -> in pic (magnetic permeability of free space) +i = current + -consider the tanget B field vectors on the overall B field lines (especially at 4 "sides") -> makes calculations easier! -tesla!
Magnetic field produced by loops -Right Hand Rule #3? +ex?
-To find the direction of the Bfield at the center of a current loop, curl the fingers of your right hand in the direction of the current. -> Your thumb will point in the direction of the field. +in pic -> dont be confused with clockwise or counterclockwise -> just remember to think of stuff "in front of you" -> dont get confused with visualizing and dimensions!
And Parallel -Two circuit components are in parallel if their? +same? +when does ∆V change? +think what? +ex?
-Two circuit components are in parallel if their two ends are at the same voltages - that is, the voltage drop is the same across both components. +same ∆V's +∆V changes ax resistors or ax voltage sources! +think nodes (same voltage areas -> must be attached to same nodes to be in parallel -> color coated in pic!) +ex: in pic
Current Loops in B-Fields -Understanding how a motor works requires understanding how? -But first, a little bit of visual convention:
-Understanding how a motor works requires understanding how currentcarrying loops of wire behave in external magnetic fields. And that means re-acquainting with an old friend - torque! -in pic!
Loops and Electromagnets -We can enhance the field produced by a single loop by? +A coil made up of several current-carrying loops is called a? -Notice how the field produced by a solenoid is similar to? -equation for B field from solenoid?
-We can enhance the field produced by a single loop by adding several loops together. A coil made up of several current-carrying loops is called a solenoid. -Notice how the field produced by a solenoid is similar to that of a bar magnet, with north and south "poles". -in pic +mew -> constant (in previous pics) +i = current +n = N / l -> number of turns / length of solenoid!
time constant and slope?
-a larger time constant -> smaller slope (magnitude) -a smaller time constant -> larger slope (magnitude) -this is true for both + and - slopes (magnitude of slopes) -a time constant -> measure of how fast the system is changing +smaller time constant -> system changes faster +larger time constant -> system changes slower
quiz 4 concept error -remember what about voltage going ax a resistor? -A current, i, is flowing through a cylindrical segment of conductive material with a shape as shown. (in pic) VA is the voltage on the left side of the segment. VB is the voltage on the right side of the segment. The material has a resistivity ρ. How can you decrease the current, i, through the segment? In answering this question, assume you can change anything about the situation through some physical means. Also assume you only change the one thing given in the answer and nothing else. Select all that are correct.
-a voltage drop occurs (voltage decreases!) going ax a resistor in the direction of the current -> keep this in mind! (voltage increase occurs when + charge goes from - to + on battery) -increase p -increase L -decrease r -increase Vb -decrease Va
Energy is key -current is flow of? +even tho? +electrons? -resistors do what? -∆V ax a resistor? -∆V ax a battery?
-current is flow of + charge +even tho - charges (the charges actually moving) are really moving opposite direction of i +electrons move opposite i (contribute to + i.... keep this in mind even tho we usually just talk in terms of i tho!) -resistors do something (with voltage drop....) -> ex: lightbulb -∆V ax a resistor -> voltage drop! (if + charge moving in direction of i) -∆V ax a battery -> voltage gain (if + charge moving from - to + end of battery)
Circuit analysis -Now we swap out R 3 and R 6 for batteries. How does the current through R 4 change? (from last pic to this pic)
-doesnt change -> same loop as before! -> always consider loops and junctions (kirchoffs rules) in circuit problems! (ask about this! different changes and what not that could be made in a problem like this!)
Frequency and wavelength -equation? -frequency of oscilating charge? -antennas? -in pic
-equation: c=λf +c is speed of light +f is frequency +lambda is wavelength -frequency of oscilating charge is equal to the frequency of the em wave that it produces! -antennas -> basically just long metal wires that can be used to generate or receive em waves -in pic -> single + charge oscilates up and down (part of i in antenna); white lines are E field lines (E field lines would be going out as straight lines if the + charge was static)
Look at bridge set questions -> lots of good ones! (got the one below wrong... careful with RHR!) -in pic
-explanation in next slide pic
Circuit analysis -If the current through resistor C is 2 A and all the resistors have R = 1 kΩ, what is the current through resistor E? -How many loops are there in this circuit? -How many junctions are there in this circuit?
-explanation in this pic and next pic! -> use kirchoffs rules to reason through! -3 loops in pic (dont forget about loops that dont include the emf) -2 junctions in the circuit
solving circuit problems?
-find the Req -> use to solve for total current or ∆V from power source / battery -trace ∆V through circuit +the ∆V changes ax resistors (drops) and batteries (increases) >drops ax resistors and gains ax batteries occur when tracing voltage in direction of current (i).... -trace i through circuit +the i changes at junctions when it splits! -remember kirchoffs loop rule and i rule!
Magnetism and circular movement? (from TA)
-if velocity of charged particle is parallel to the B field -> charge experiences no force -if velocity of the charged particle is perpendicular to the B field -> charge experiences only a circular force -if velocity of a charged particle is not perfectly perpendicular or parallel to the B field -> charge experiences circular force and moves in direction (would move in direction of parallel velocity vector!)
More with Induction -If I pull the magnet up along the same path, which quantities reverse?
-in pic
Review: EM Waves -What is the frequency of this wave? -What is the amplitude of the electric field? -What is the intensity of this wave?
-in pic
Review: Electromagnetic Waves -main ideas and equations?
-in pic
Review: RC Circuits -The capacitor is initially uncharged. When the switch is closed, what is the initial current through the resistor, and what is the current after a long time has passed?
-in pic
Sunshine up close -The Sun outputs 3.85 x 10 26 W in the form of EM waves. If the radius of the Sun is 7 x 10 8 m, what is the intensity of EM radiation at the surface of the Sun? +explain?
-in pic +sun distributes power over the 3D sphere area around it! use intensity equation!
Lecture 7b Hand waving -How does this image symbolize the relationship between electric and magnetic fields in an electromagnetic wave? -what makes an em wave overall?
-in pic -making an em wave +changing B field induces an E-field (changing B field results in change in magnetic flux -> induces emf -> induces E-field) +changing E field incudes a B field +thus changing E and B fields combine to form an reinforce one another and make an EM wave (oscilatory, reinforcement of E and B fields by each other!)
More with Induction -In what direction is the magnetic force on the magnet from the copper sheet when I push the magnet down? +important explanation!
-in pic +ask about?? +think about the B field at the center of the loop as a magnet (think of B field inside magnet is same as B field induced in current carrying loop) -> consider the forces that the 2 "magnets" would inflict on each other (like poles repel and opposite poles repel) -> determine forces from there! +if they attract (same poles) -> forces (of magnet on other magnet) will point toward each other +if they repel (different poles)-> forces (of magnet on other magnet) will point away from each other
Evolution with time (charging) -table and ideas?
-in pic +close switch and time increases -> i in circuit decreases and q increases on capacitor
Proton beam math -Protons (m p = 1.67 × 10 -27 kg) being used for a therapy treatment have a velocity of 1.5 × 10 8 m/s and need to be bent in an arc of radius 1.2 m. What strength of magnetic field is necessary to bend the proton beam?
-in pic +eqs usage (last slide)!
Field due to solenoid -Let's model an MRI machine as a solenoid with length 2 m operating at a current of 100 A. If the field inside the machine has magnitude 3 T, how many total turns must the solenoid have?
-in pic +equations!
Frequency and wavelength -In the picture shown, the house antenna is 200 m from the station antenna. What is the approximate frequency of the radio waves? +explain? -amplitude of E and B field with distance?
-in pic +estimate the wavelength by looking at figure and solve using equation! -amplitude of E and B field -> decrease with increasing distance! (check this??)
Example: Induced emf -A square loop enters a uniform magnetic field B = 2.0 T at a constant speed v = 1 cm/s. What is the magnitude of induced emf in the loop? +Explain?
-in pic +in pic +or just use the emf(motional) = lvB (l is the length of the object thats proportion is not changing in the B field....∆X is changing and l is not....) -> in pic!
Ohm's Law as a "flow rate" -equation? +analogies? -resistance equation? -In all cases?
-in pic +in pic (ex: water through garden hose, flow rate is higher with a high pressure difference.... just like current flows faster with a higher ∆V) -in pic +resistivity (p) -> higher in insulators! -In all cases, the flow of something (𝑖 , 𝑄 , 𝑃𝐶) is driven by a gradient (Δ𝑉 , Δ𝑃 , Δ𝑇) and met by a resistance (all involving length divided by area).
Applying Lenz' Law -A conducting rectangular loop moves with velocity long straight wire as shown. In which case does the induced current flow in the counterclockwise direction? +Explain?
-in pic +must oppose the original change in flux; either "oppose" or "fill in" the original change in flux!
Power vs. Intensity -A point source of radiation emits power 𝑃 * uniformly in all directions. A detector of area 𝑎 1 is located a distance 𝑅 away from the source. What is the power 𝑃 received by the detector? +explain?
-in pic +power emitted from source is constant but is spread out over a 3D shell (area) -> power is experienced by the area given +power is distributed over an area of 4(pi)r^2 and experienced by object with an area of ad (on picks up fraction of power released from the source because power is spread over an area!)
Magnetic Force & RHR -B force equation ? -only B force (FB) on charged particles when? -determining direction of the B force on the charged particle? -B field in pic?
-in pic +q is the charge of the partcile moving in the B field (just do absolute value bc B force is a vector anyway!) +v is the velocity of the charged particle +B is the magnitude of the B field +sinø where ø is the angle bw B field lines and v of the particle -only B force on charged particles in a magnetic field when +particles are charged and moving (static charges dont experient a B force) +component of the velocity of the charged particle is perpendicular to the B field; sinø is only used in equation to find the component of the velocity that is perpendicular to the B field! +if B field and V are parallel (or anti parallel) -> B force is 0 (ø is 0) -use RHR-1 (right-hand rule 1) to determine direction of the B force! -> this is direction for a + charged particle (direction is opposite for a - charged particle!) +thumb in direction of the v +fingers in direction of the B field +palm points in direction of the B force +COULD ALSO DO (fingers in direction v, palm in direction of B field, and thumb in direction of B force -> cant get tricky tho... use above option!) -B field in pic is uniform +B fields are often treated as uniform for calculations in this class (even those uniform B fields are not common in nature...??)
Lab this week -in pic
-in pic +wire coils to produce B field +electron source +electrons follow circular path!
Torque on a current loop -demo? +Explain?
-in pic (i is clockwise!) +use RHR-1 on each side of the loop -> see that loop will rotate clockwise! (go toward top blue arrow in pic!)
Magnets and loops -At this instant, which bar magnet orientation best represents the magnetic field created by the loop of induced current? -B field at center of (current carrying) loop?
-in pic (loop will repel magnet in pic!) -think of B field at the center of a (current carrying) loop as the same as the B field inside of a magnet (S->N inside a magnet)
Electromagnets -Two current-carrying wire loops are oriented as shown. Which picture of two magnets will best predict the forces on these two loops? +explain?
-in pic -> We didn't get to this question - try it on your own. +RHR # 3 tells you the direction of the B field from each loop. A current-carrying loop is a magnetic dipole - its field looks like that of a small bar magnet. -think of the B-field in the center of a current carrying loop as the same as the B field inside of a magnet +B field inside of a magnet goes from S -> N +B field around a magnet goes from N -> S
Loops in Fields -In which case will the loop rotate around the y-axis? +explain?
-in pic -> case 1 +find B force direction using RHR-1 on each side of the loop -> determine how it would rotate from this information! +We didn't get to this one either - it's related to one of the Bridge Set questions. You can use RHR #1 on each segment of the wire, or recognize that the square loop is a magnetic dipole that wants to orient Itself so its B field is parallel to the external B field.
Fields & Forces (again) -demonstration set up? -Now we submerge the plates of the capacitor in a beaker of pure (deionized) water. Will there be a current? -Now we add salt to the water. Will there be a current? -current is in what direction? +ex +? +ex -?
-in pic -> light bulb with copper plate below; something is needed to transmit charge between the copper plates and "complete the circuit" for the lightbulb to go on +lightbulb -> resistor that heats up when current goes through it +∆V -> power source (battery, often called emf) -NO -> DI water is pure water with no ions -> thus there are no free charges (carriers) (ions usually carry charge) and the charge cant move (no current!)... (think the - charge ends up on left side of plate but there arent any charges that can move in water to carry charge current through water) -YES -> NaCl dissolves into constituent ions which can act as charge carriers (current occurs). Charge (carriers) allow the charges to flow between the plates and complete the circuit.... (think the - charge ends up on left side of plate and there are charges that can move in water to carry charge current through water) -current -> flows in + direction +ex: + charge flowing in direction that + wants to flow is + current +ex: - charge flowing opposite direction that + would want to flow is + current
Discharging capacitors -After the capacitor has been fully charged (when the switch S is closed) switch S is opened. +What is the time evolution of the charge on the capacitor? +What is the time evolution of the current through the resistor?
-in pic -> new loop forms in which capacitor supplies current going in loop to the left (in pic) -> battery is no longer connected to the circuit and thus provides no current! +charge on current decreases over time +current in new loop decreases over time
Equivalent resistance -If ε = 20 V and all the resistors have a resistance of 1 κΩ, what is the current through the emf source (battery)? +how to?
-in pic and next pic +consolidate the circuit until just one resistor and then find the current if you know the ∆V of the battery +use rules regarding how series and parallel resistors relate to one another! (in pic!)
Current Loops in B-Fields -In which direction does the torque rotate the current loop? +explain? +This effect is how? -equation for B force on current carrying wire?
-in pic! +use RHR-1 to find direction of B force on parts of current loop (magnetic force could cancel but torque is still present!) +This effect is how electric motors work - see this YouTube video for details -in pic!
B-field lines from a permanent magnet -Here's a bar magnet and an array of small compasses. The tips of the compass arrows are their North poles. Which end of the magnet is its North pole? explain? -B field vectors relation to B field?
-left end -> opposite poles are attracted to one another and thus the N pole of the compass must be attracted to the S pole of the magnet -B field vectors are tangent to the B field lines -> in pic (important for problem solving!) +going into S pole of magnet -> would be straight line pointing into magnet (in pic) +cominng out of N pole of magnetic -> would be straight line coming out of magnet +going from N to S pole outside of magnet -> would be line directly left (in pic, top or bottom would be same!)
𝑞(𝑡)=𝐶𝜀(1−𝑒^−𝑡/𝑅𝐶) -max value part of eqs? -form and exponential part of eqs?
-max value part -> C𝜀 +smaller max value means this has smaller value... -form and exponential part (slope part) -> (1−𝑒^−𝑡/𝑅𝐶) +smaller slope means this has smaller value -After a long time, the exponential term in q(t) approaches zero and q(t) approaches its maximum, asymptotic value of Cε . Decreasing the power supply voltage ε by half also decreases the capacitors' maximum charge by half. However, it is the exponential term that determines the shape, or profile, of the curves, and the exponential term only depends upon the values
Magnetic Flux -what does magnetic flux need? -equation? +other form? +variables in eqs? -tilting angle?
-needs B field and surface for B field to pass through -in pic +eqs is really just magnetic flux = AB(perpendicular); A multiplied by the portion of the B field that is perpendicular to the A of the surface +A is area +B is B field strength +ø is the angle bw the perpendicular of the surface area and the B field -> in pic! BE CAREFUL and make sure to use the correct ø -tilting angle (right bottom side of pic) -> captures less and less B field lines through it until no B field passes through (this occurs if ø changes from 0 -> 90)
phase angle -explain idea?
-phase angle (ø) is the angle formed when you do not start at the general starting point, and is how far off you start from your starting point. +ex: sin(0 + ø) = 1 -> so ø would have to = pi / 2
movement of charge in a B field with velocity vector components that are parallel and perpendicular to the B field? neutral object in a magnetic field?
-the charge will move in a helical pattern (due to V component that is perpendicular to the B field) and in the direction of the V component that is parallel to the B field (not affected by magnetic field and thus velocity carries on this way)... moves NOT in direction of overall velocity vector, BUT in direction of the parallel component of velocity! +in pic -neutral objects (NOT neutral particles, but neutral objects!) -> have lots of + and - charges in them -> + and - charges both experience the same B force but in different directions (plane ex and separation of charge -> ∆V is created....polarization idea?)
i in parallel RC circuit?...bulb.goes.from.dim.to.brighter(in.parallel.RC....)??
-the i starts off splitting bw the two paths (one to resistor and other to capacitor. -the q of capacitor increases to its max and i can no longer flow toward it (think of + shield kind of that redirects current) -all i then flows down the middle to the resistor (bulb goes from dim to brighter in this ex) *the i from capacitor cant come back and combine (if discharged..??) -> just redirects the original full current to the middle *the capacitor discharges (and disconnect from battery...) -> i is - and goes in opposite direction (when ∆V source is disconnected).... new circuit loop basically...!
Review: Circuit analysis -A circuit contains two batteries (ε1 =10 V and ε2 =20 V) and two resistors (R 1 = R2 = 10 Ω) as shown. What is the current i supplied by battery 1?
-use loop and junction rules to solve this! +in pic
Lecture 5a -This bird is perched on an active electric fence. Why is it safe for it to do so?
-very small (almost no) potential difference (∆V) bw birds feet and thus current cannot flow through bird and bird is not shocked +must have ∆V for current to flow! +human on ground and hold wire -> large ∆V -> i flows and person is shocked! +in pic
Circuit diagrams 1. The circuit symbols we will use are? 2. We assume that wires have no? 3. Wires can be? -positive and negative depiction of ∆V source?
1. The circuit symbols we will use are shorthand for physically real things (simple circuit is shown in top pic -> just battery with wires and 1 resistor) 2. We assume that wires have no resistance and so there is no voltage drop (and therefore, potential energy loss) across a wire -assume ∆V's only occur ax batteries and resistors! -assume circuits are ideal! -voltage source -> usually a battery but could be some random voltage source! 3. Wires can be reshaped and stretched at will -dont shift junctions in circuit elements -ex: in pic -positive end -> longer line (higher potential) -negative end -> shorter line (lower potential)
Particle paths in magnetic fields -3 different paths that a charged particle could follow in a B field (all for uniform magnetic field....?) -only what about v matters for B force?
1. v of charged particle is perfectly parallel (or antiparallel) to the B field -> particle moves in direction of velocity vectors and experiences no B force -the sinø = 0 2. v of charged particle is perfectly perpendicular to the B field -> particles experiences (maximum...?) B force and moves in uniform circular motion -the sinø = 1 3. v of charged particle is bw parallel and perpendicular to the B field -> partilce moves in spiral pattern; sinø is bw 0 and 1 -particle has v component that parallel to the B field and thus moves in direction of v of particle (this components experiences no B force) -> particle moves in v(parallel) direction -particle also has v component that is perpendicular to the B field and thus experiences some circular motion (this component experiences a B force!) -angle with field traces a helical pattern -> in pic! -can you use r eqs here?? -only component of v perpendicular to the B field matters for calculating the B force -> sinø is just used in equation to help you find this component! +vsinø = v (perpendicular component)
Induced emf -A magnet is moved toward a loop as shown. Three trials are run: a copper loop, a rubber loop, and no loop at all (empty space). +In which case will the induced emf be the greatest? +In which case will the induced current be the greatest?
A magnet is moved toward a loop as shown. Three trials are run: a copper loop, a rubber loop, and no loop at all (empty space). +emf (induced emf here) -> same for all -> independent of material! +current -> greatest for copper (i flows the best in the best conductor!) (i = ∆V / R and R is the lowest in the copper!)
Resistors and "hallways" Charge carriers will lose more electric potential energy after passing through which resistor?
A) Resistor 1 -higher resistance and same current produces a larger ∆V and thus since ∆Uelec = q∆V -> ∆Uelec is larger in resistor 1 and more electric potential energy is lost!
Cool websites -> answers to below questions are on here! https://www.epa.gov/ghgemissions/understanding-global-warming-potentials https://science.nasa.gov/ems What sort of electromagnetic radiation would you want to use in order to survey the health of crops in a particular region from orbit? Check out this website then answer the following question: Tour of the Electromagnetic Spectrum Consider the following greenhouse gasses: Carbon Dioxide, Chloroflourocarbons, Nitrous Oxide, and Methane. Which greenhouse gas will trap the most longwave radiation? (You can start your search by visiting this website.)
Cool websites -> answers to below questions are on here! https://www.epa.gov/ghgemissions/understanding-global-warming-potentials https://science.nasa.gov/ems What sort of electromagnetic radiation would you want to use in order to survey the health of crops in a particular region from orbit? -near infared waves Check out this website then answer the following question: Tour of the Electromagnetic Spectrum Consider the following greenhouse gasses: Carbon Dioxide, Chloroflourocarbons, Nitrous Oxide, and Methane. Which greenhouse gas will trap the most longwave radiation? (You can start your search by visiting this website.) - Chloroflourocarbons
Current will always follow the? -choice bw two paths with different batteries (emf's) on either path? -choice bw two paths with 2 different resistors? -two currents seem to be coming at each other, which one wins?
Current will always follow the EASIEST path (for the most part...) -choice bw two different emf's -> ALL current will go toward the emf with the higher voltage! -chioce bw 2 different resistors -> more current will go toward the resistor with lower resistance but some current will still flow toward resistor with higher resistance -stronger current will dominate and then all current will go in that direction
Fields & Forces (again) An electron is somewhere between the plates of a capacitor connected to a battery. What happens to the electron when we release it? (The space between the plates is vacuum. Ignore gravity.) -> in pic? -explain? -comparison with gravity? +but charges are always? +sphere in glycerol vs water? +sphere in glycerol (or water??) velocity? +charge carriers in real substances?
D) Accelerates to the right -An electric force pulls the electron to the right and thus bc there is a force the electron must be accelerating (F=ma) -isolated electron moving to the plate is like a falling body with gravity (accelerating from force) +but charges (Charge carriers) are constantly hitting stuff when they travel (resistance!) +sphere takes longer to reach bottom in glycerol than water bc there is more resistance in glycerol +sphere moves at roughly a constant velocity bc the F down from gravity is balanced by the force up from viscosity and Fnet is about 0 +charge carriers in real substances -> move at about a constant velocity (charges would accelerate in a vacuum with nothing else present, but in real material/susbtances they hit other stuff and slow down and Felectric is balanced by Fresistance and Fnet is about 0 and thus they move at about a constant velocity)
Circuit analysis -If ε = 15 V, R 1 = 2 kΩ, R 2 = 600 Ω, R 3 = 10 kΩ, R 4 = 300 Ω, R 5 = 2.5 kΩ, and R 6 = 700 Ω, what is the current through R4 ? (in pic)
E) 50 mA -apply simple kirchoofs loop rule to this circuit!
∆Vcap in RC circuit equation? -the ε in equation? -same idea?
If you refer to the "Useful Equations" on the "Circuits II" discussion worksheet, in the equation for charging a capacitor, ΔVcap(t)=ε(1−e−t/RC), ΔVcap refers to the voltage difference across the capacitor. -the ε is the emf of the battery. -It's the same idea in the equation for discharging a capacitor.
Forces between current carrying wires
Let's see that with real wires and current -> in pic
22.3 Magnetic Fields and Magnetic Field Lines -magnetic field line rules?
Magnetic fields can be pictorially represented by magnetic field lines, the properties of which are as follows: The field is tangent to the magnetic field line. Field strength is proportional to the line density. Field lines cannot cross. Field lines are continuous loops. -they add if in same direction and cancel if in opposite directions just like vectors!! -> consider components too!
M3 Question 3A current flows through a 100 Ohm resistor. Which equation would be the simplest to use to find the power dissipated by the resistor?
P=i^2R -use the given variables!
Question: Wires create magnetic fields true or false?
Question: Wires create magnetic fields FALSE -> moving charges (within the wires) create the B fields, NOT the wires themselves!
negative exponents
Raising a number to a negative exponent is the same as raising the number's reciprocal to the equivalent positive exponent -> in pic
Resistors and "hallways" The current will be greater through which resistor?
Resistors and "hallways" C -> same -We didn't get to this in class, but the current is the same everywhere in a circuit. -> current is same everywhere in a series circuit... not in parallel tho?? -> this shows series!
Summary · Electromagnetic induction takes place when a? o This emf can be a? o Or? · Lenz's law? · Faradays law can be?
Summary · Electromagnetic induction takes place when a changing magnetic flux through a surface generates an emf around the border of that surface (described by Faraday's law) o This emf can be a motional emf -> generated when a conductor is in motion and B forces act on the charges in the conductor o Or induced emf can be created when B forces cannot be present and only electric forces act on the charges to create a current · Lenz's law -> tells us direction of induced emf and resulting current (induced B field too) · Faradays law can be used to explain how AC generators produce alternating current in pic!
Visualizing Plane Waves -The graphs we are showing are? +why?
The graphs we are showing are deceiving +the E and B fields fill up a volume (fill up space) -> in pic!
in pic -> voltage drops experienced by different resistors?
The resistors in Circuit C are connected in parallel, which means that all three resistors share the same potential, or voltage, drop. Because the parallel combination of resistors is connected to the emf source, all three resistors have a potential drop equal to the emf potential 𝜀ε . Likewise, the lone resistor in Circuit D is connected to an identical source of emf as in Circuit C. Thus, the potential drop across the resistor is also 𝜀ε . Therefore, the potential drop across all four resistors in both circuits is the same. -> in pic (think of loop rule to understand this -> each loop must have a voltage drop that can cancel out the emf!)
Question: Three cases involving identical forces acting on identical sticks are shown in the figure. Compare the magnitudes of the torques about an axis through the center of the sticks. -> in pic
Torque(A)>Torque(B)>Torque(C) +In pic -> important!
Drift speed? -electron movement in objects? -equation?
Vd = average speed of electron to move down a wire (Vd is usually very small bc electrons make a lot of collisions when they move) -electrons bounce around randomly off fixed + ions (moving fast and random) -> takes a long time for electrons to slowly move through the wire -equation -> in pic!
in the review guide it says, "Relate the intensity of an EM wave to the amplitude or average value of the E- and B-fields that compose it." does the average value of the E and B fields refer to the rms or? -referring to average values here?
Yes. And you won't have to worry about rms, so just relating intensity to E0 and B0 is all you need (for exam 2 atleast!) -the average values of the E and B fields -> refers to the rms values of the E and B fields (at least in this context)....
Prelecture 7b [MUSIC PLAYING] NARRATOR: We're used to science fiction. It's common to be entertained by heroes using invisible forces to do incredible things. But is this concept really far-fetched? The truth is our world is actually saturated with invisible energy that can be harnessed and used to accomplish amazing feats that seem to come straight from the pages of a comic book. This energy can be found within? The spectrum is a? You can see from this image that on one side of the spectrum is radio waves with a wavelength of up to 100 kilometers. While on the other side is gamma rays with wavelengths as small as 10 to the negative 6 nanometers. There is an abundance of marvelous science that occurs within each of these regions. And we'll cover more of this later. But for now, let's focus on the visible spectrum. To do that, we have to? If you do the math, that means the human eye can only see? Right off the bat, our eyelids would no longer work and sleep would be impossible, since X-rays would penetrate our eyelids. Also, all of those beautiful colors we enjoy would be drowned out by a sea of red from everything that has a temperature. Even in the dead of night, our vision of the universe would look something like this. As it turns out, our eyes are? Human eyes aren't the only things that respond differently to different wavelengths of light. So does the atmosphere. And this gives rise to an important phenomenon known as? Like all waves, light from the sun carries energy across space to the Earth. Some of this energy is reflected by clouds or by the surface of the planet back into space. A bit more is absorbed by the atmosphere. The fact that the ozone layer in the stratosphere absorbs? The sunlight that gets through the atmosphere and? Those objects? While certain gases like carbon dioxide will let visible wavelengths pass? [MUSIC PLAYING]
[MUSIC PLAYING] NARRATOR: We're used to science fiction. It's common to be entertained by heroes using invisible forces to do incredible things. But is this concept really far-fetched? The truth is our world is actually saturated with invisible energy that can be harnessed and used to accomplish amazing feats that seem to come straight from the pages of a comic book. This energy can be found within the electromagnetic spectrum. The spectrum is a range of waves that are categorized by their wavelength and frequencies. You can see from this image that on one side of the spectrum is radio waves with a wavelength of up to 100 kilometers. While on the other side is gamma rays with wavelengths as small as 10 to the negative 6 nanometers. There is an abundance of marvelous science that occurs within each of these regions. And we'll cover more of this later. But for now, let's focus on the visible spectrum. To do that, we have to zoom all the way into the small region of wavelengths that are between 700 and 400 nanometers. If you do the math, that means the human eye can only see 4/10 millionth of a percent of the available waves in our atmosphere. At first, that might sound discouraging. If we could see more, wouldn't that make the world more colorful? Not so fast. If your range of visibility improved by a mere 3/10 ten-thousandth percent. We would be able to see some X-rays and infrared. Right off the bat, our eyelids would no longer work and sleep would be impossible, since X-rays would penetrate our eyelids. Also, all of those beautiful colors we enjoy would be drowned out by a sea of red from everything that has a temperature. Even in the dead of night, our vision of the universe would look something like this. As it turns out, our eyes are finely crafted instruments that are calibrated precisely for us to function on planet Earth. Human eyes aren't the only things that respond differently to different wavelengths of light. So does the atmosphere. And this gives rise to an important phenomenon known as the greenhouse effect. Like all waves, light from the sun carries energy across space to the Earth. Some of this energy is reflected by clouds or by the surface of the planet back into space. A bit more is absorbed by the atmosphere. The fact that the ozone layer in the stratosphere absorbs the bulk (97-99% of the suns medium frequency ultraviolet light) of the sun's ultraviolet radiation, which would kill plants and plankton, makes life on earth possible. Of course, some UV rays do pass through, and they're responsible for the sunburn you get every time you stay out in the sun too long. The sunlight that gets through the atmosphere and heats up everything on the Earth. Those objects, whether rocks or cars, give off electromagnetic waves in the infrared region. This means shorter wavelength rays (light coming from sun) get transformed into longer wavelengths (infrared radiaiton going out from objects that were heated by sunlight), and that makes all the difference. While certain gases like carbon dioxide will let visible wavelengths pass, they reflect the longer infrared wavelength back toward the earth. The more greenhouse gases like carbon dioxide in the atmosphere, the more heat gets trapped. In the end, this type of electromagnetic radiation makes a world of difference. [MUSIC PLAYING]
consider things from multiple different? -break down stuff?
angles and perspectives! -always determine the best perspective to solve the problem! +ex -> in pic -> look for forces and perspectives that would make it rotate around x-axis! -often helpful to think of situation as right in front of you! -break down stuff into different parts of loop and always consider how your viewing it; ex: case 1 -> RHR would have the fingers down and palm to the right bc that's how your viewing it (when considering left side of rectangle for force!) -> often helpful to put the paper out in front of your face... dont confuse self with perspectives...!! +ex: RHR for case 1 -> consider each side to determine forces on each side and if or how its rotating! -may help to think of page as in front of you!
idea with equivalent resistance and how to treat resistors?
can find an equivalent resistance using series and parallel rules and then just treat the combined (originally separate) resistors as one resistor with the new equivalent resistance basically
current will follow? -ex?
current will follow the path of least resistance -ex: if the path of a current splits and the resistors are the same on each new path -> = amount of current will go down each path +more current will go down paths will less resistance tho! -> use equations to determine amount that will go down paths!
Vd and I are in the same? pic last slide
direction! pic
· Question -> A wooden loop and a wire loop, both with the same shape and size, are placed next to the north poles of identical magnets. Then, the loops are moved closer to and farther from the magnets in exactly the same way. The emf generated around the wooden loop is -o Notice that the loop material is?
equal to the emf generated around the wire loop. -explanation in pic -Notice that the loop material is not included in the magnetic flux expression or in Faraday's law. An emf is generated around any loop that experiences a change in magnetic flux, regardless of the material of the loop. In fact, an emf is induced by a changing magnetic flux even in the absence of any physical loop. Therefore, the emf generated around the wooden loop is equal to the emf generated around the wire loop.
using loop rule to solve for variables -moving across emf source? -moving across resistor?
find a good loop and analyze! -moving across emf source +voltage increase (+) if move across emf source from - to + in loop direction +voltage decrease (-) if move across emf source from + to - in loop direction -move across resistor +voltage decrease (-) if move across resistor in direction of current +voltage increase (+) if move across resistor in opposite direction of current -ex: in pic!
general rule that?
general rule that you cannot use a wave to detect anything that is smaller than the wavelength of the wave! -ex: smallest object you could see with visible light is about 400 nm bc shortest wavelength of visible light is about 400 nm
Passive membrane model ?
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Review: Agenda for today
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Review: RC Circuits -main ideas and equations?
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Today's agenda
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What's oscillating today
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chapter summary
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last slide pic
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overview of what we covered
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review: Circuits -main ideas and equations?
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review: Current & Resistivity -main ideas and equations?
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review: This week...
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review: main topics
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todays agenda
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Properties of Waves In the wave shown, the wavelength corresponds to _____ and the amplitude corresponds to ___ -explain?
in pic -wavelength -> in pic -amplitude -> in pic (0 to peak, either crest or trough as peak) -the 3 in pic -> would be 2x the amplitude
The Electromagnetic Spectrum -Which of the following has the greatest frequency?
in pic +equation and general knowledge
Exponential Primer? -We'll be taking exponents of? -Note that "approaches ∞" is another way of saying?
in pic -We'll be taking exponents of e = 2.71828 -Note that "approaches ∞" is another way of saying really, really big.
Evolution with time: graphing -main ideas?
in pic -close switch and time increases -> i in circuit decreases and q increases on capacitor +i refers to i in circuit +q refers to charge on capacitor +use equations
good HW question -draw what to help?
in pic -draw the B field vectors on the "flat parts" of the B field lines to understand where they could add or cancel! (drawn on previous slides from lecture, slide 209 for ex) -larger currents have stronger B fields (logic in this problem -> large current B field far from larger current could cancel a small current B field that is close to the small current -> leads to B field being 0 (at this location) if the B fields are also in opposite directions at this certain location....)
22.11 More Applications of Magnetism -the v and E and B fields??
in pic -if v is perpendicular to both E and B fields -> use equation below to determine its magnitude!
todays agenda -we are not covering?
in pic -in pic!
22.7 Magnetic Force on a Current-Carrying Conductor -The magnetic force on current-carrying conductors is given by?
in pic -put fingers in the direction of I (just like you did with v) -> and then palm in direction of B field -> thumb points to magnetic force direction!
22.9 Magnetic Fields Produced by Currents: Ampere's Law -long wire? -loop? -solenoid?
in pic -soleniod doesnt depend on radius!
22.8 Torque on a Current Loop: Motors and Meters The torque 𝜏 on a current-carrying loop of any shape in a uniform magnetic field. is?
in pic -the 𝜃 is the angle between the perpendicular to the loop (plane) and the magnetic field.
22.10 Magnetic Force between Two Parallel Conductors -The force between two parallel currents? -The force is attractive if?
in pic -to determine if attractive or repulsive -> can also draw out the magnetic field and then remember that outside of a magnet, the magnetic field goes from N to S poles and then remember that opposite poles attract and like poles repel -> do it this way!
Example walk through Rms =? Intensity can be calculated with rms value of E field -> rms value of E field can be calculated from amplitude of E field By comparison -> intensity of suns radiation on earths surface -> is about 1360 W/m^2 -> so radio transmission and reception equipment is actually quite sensitive!
in pics
be careful with sinø in?
in torque equations with magnetic field - the ø=90 means that B field and plane (current...?) are parallel -> torque maximized - the ø=0 means that the B field and the plane (current...?) are perpendicular... -> torque minimized -the 𝜃 is the angle between the perpendicular to the loop and the magnetic field.
increasing flux by changing area? -think what -ways to change flux? +increase it? +Decrease it?
increasing or decreasing area can change flux -increase area to increase flux -decrease area to decrease flux -think of how much total B field is passing through a given area; more B field passes through a given area -> higher flux! +thus, changing B field, changing area, or changing angle can all change the flux bc all these changes can change the amount of B field that is traveling through a given area! -change flux -> change area, B field, or theta (ø) -> (think what can change the amount of B field passing through the enclosed space!) +increase flux -> increase B field going through, increase A (more B field can pass through enclosed space), change ø to allow more B field to pass through (think what can cause the enclosed space to have more B field pass through it) +decrease flux -> decrease B field going through, decrease A (less B field can pass through the enclosed space), change ø to allow less B field to pass through! (think what can cause the enclosed space to have less B field pass through it)
B-field direction on long current carrying wire vs B-field direction on current carrying loop?
long current carrying wire -> easiest to use RHR-2 -thumb in direction of current and B-field is in direction that fingers curl! (think of B-field vector tangents at each 4 sides too!) current carrying loop -> use RHR-3 -curl fingers in direction of the current and B field is in direction of thumb!
always look at?
look at book summaries in open stax! and discussion material!
question · Consider the circuit shown (in pic) · What will be the current through the resistor a long time after the switch S is closed?
o ϵ1R -> ∆V of R must be = top the ∆V of battery to obey kirchoffs rule! § Equations for problems like this are mainly used when the resistor and capacitor are in series... parallel is different...??
solving with kirchoff's rule?
often need to guess the current direction to start.. -if current comes out to be negative -> you guessed the wrong current direction (magnitude will still be the same, just flip the sign!) +could restart analysis or just continue (just be consistent) -ex: in pic -> i2 is shown in the wrong direction in pic! -label currents according to where their corresponding resistor is -> in pic! (Ex in pic -> i3 is where the R3 is) +NOT necessarily where their corresponding emf source is... -> in pic -use loop and junction rules!
finding equations? -whats important?
often should look at physics 104 prelecture notes on word if cant see equations in quizlet pics! -also look at end of chapter summaries -> important!
look at bridge set questions on docs notes! -consider question in pic and others in notes!
on docs! -yes ! In the second diagram, the addition of the wire before resistor C provides a path back to the emf source that does not have any (or very little) resistance. All of the current I will take the path of no resistance, which makes the current through resistor C zero (𝐼c=0). Thus, the power dissipated by resistor C is also zero (Pc=0) . Therefore, the addition of the wire changes the power orderings. +current takes less resistant path if available in general??
cylinder/wire cross sectional area formula?
pi(r^2)
chaprter summaries
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chapter summaries
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pic lasrt slide
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pic -view membrane as capacitor!
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pic -> important equation!
wire placed parallel to another wire that is generating EM waves with an AC generator? heating up objects with EM waves? resonance frequency?
reception will be best received in the wire when the receiving wire is parallel to E field being emitted by the sending wire -> (electric force causes charges in wire to move up and down and thus induces current) and because the B fields are arriving perpendicular to the wire (magnetic force on charges in wire causing them to move up and down and thus induces current) -The receiver antenna should be oriented perpendicular to the axis of propagation, and along the axis of oscillation for the electric field. Therefore, the antenna should be oriented parallel to the z-axis in cases 1 and 3, and parallel to the y-axis in case 2. -> in pic! -EM waves can be used to heat up objects because they cause molecules/charges in substances to oscilate which ultimately produces heat (molecular vibration produces hear!) resonance frequency -> frequency of EM waves at which an oscillator can most effectively absorb EM waves -waves are either primarily reflected or transmitted at other frequencies (and little is absorbed)!
good problem solving technique?
substitute random numbers (usually do 4) with problems that just give variables -> especially helpful with finding ratios and what not!
determing if resistors are in series? -current idea? determining if resistors are in parallel? -node idea?
they are in line with one another -> current is the same and thus there must not be any area where the current can split between them! -current changes when you hit an area where the current can split (more current will go down the path of least resistance!) they have the same voltage and thus they must be connected to the same nodes -nodes -> areas with the same voltage basically (think forward and backwards when determining nodes!!) -> voltage changes when you move ax a resistor or a voltage source!
think of B field at the center of a current carrying loop? -explain? -ex?
think of B field at the center of a current-carrying loop as the same as the B field inside of a magnet! -B field inside of magnet goes from S -> N -B field outside of magnet goes from N -> S -ex: in pic!
for RC circuits?
use old capacitor equations (from unit 1) to solve for energy of capacitor and other variables and what not!
· Ex -> in uniform B field -> just find ∆flux by flux (final) - flux (initial) and then use eqs's! o Angle and area are constant o Calculate the emf -> not a huge voltage, enough to make current if loop is conducting material § Will learn to determine that the indcuced current in this ex would be in the coutner clockwise direction!
walk through of ex -> in pics!
resistance of voltomer? -voltages with batteries idea?
want it to be high... -in pic -> high resistance (a in pic) -The voltmeter being parallel to the resistor will cause the current to split, thus, it will change the total current of the circuit. We want the change to be as small as possible, and to do that, the resistance of the voltmeter needs to be very big. Let the current goes in the junction of second resistor and the voltmeter be I_total, the current goes through the second resistor be I_2, the current goes in the V to be I_v. To get I_2, we write the equation, I_2=[R_v/(R_2+R_v)]*I_total. if R_v is significantly bigger than R_2, the fraction is close to 1, thus I_2 would be very close to I_total. -voltage going into a battery does necessarily have to start at 0 V ....
when do objects travel the exact same path in a mass spectrometer?
when they have equal mass:charge ratios (m/q) -the r = mv/qB. r is radius of circular path that particle will travel +v and B can be set to constant value +changing sign of q flips direction that the charge will travel. changing value of charge will change distance that +changing mass changes the distance that the particle travels!
idea with (large) neutral object?
with a (large) neutral object -> there are lots of + and - charges within the object -forces can be felt and experienced individually by these separate charges -> consider for movement of charges and whatnot when a (large) neutral object (With lots of + and - charges comprising it) is placed into an electric or magnetic field +think airplane example in discussion! -THIS IS DIFFERENT FROM A NEUTRAL PARTICLE WHICH WOULD NOT EXPERIENCE ELECTRIC OR MAGNETIC FORCES
· Consider the 2 circuits shown in pic; how do currents and power in these 2 circuits compare? -> in pic -> important problem solving in this ex! -work through? -big idea?
· Consider the 2 circuits shown in pic; how do currents and power in these 2 circuits compare? -> in pic -> important problem solving in this ex! o Resistor in series circuit § Apply kirchoffs loop rule starting wit the battery -> voltage gain by battery and voltage drop ax each resistor § Bc its in series -> battery and 2 resisors all have same current through them · Rearrange expression to solve for current in circuit -> in pic § Now that we know current through each element of the circuit, we can calculate the power deliver by the battery · Since we know current through and resistance of both resistors -> can calculate power dissipated by 2 resistors · Total power dissipated by resistors is equal to the power delivered by the battery (conservation of energy.. .kirchoffs rule) · In pic o Resistors in parallel § First determine the equivalent resistance of the two resistors §Now with just battery and single equivalent resistance in the circuit we again apply kirchoffs loop rule with a voltage gain over the battery and a voltage drop over the equivalent resistance and rearrange the resulting eqs to solve for the total currents in the circuit (condense series in parallel always or why??) -> in pic § Calculating the power deliver by the battery, we see that when the resistors are attached in parallel, the battery must deliver electric energy to the circuit more quickly than in the series situation -> in pic § To calculate current through each resistor, recall that voltage drop ax individual resistors in parallel is the same as the voltage drop ax the Requiv, which is 12 V in this case -> in pic § Use ohms law to calculate current through each resistor · Currents obey kirchoffs junction rule; the total current through the battery is equal to the sum of the currents through the resistors -> in pic § To calculate power dissipated by each resistor -> use choice of power equations -> in pic · We see that total power dissipated by two resistors is equal to the power delivered by the battery § Summary pic · big idea -> find what you know to be constant and then use rules about circuits in series and parallel as well as kirchoffs laws to reason through problems!
· Consider the set up in pic -> what happens when the switch is closed? -> in pic o Begin by calculating the? § According to expressions for charging capacitor, at t=0, the current is = to? § Charge on capacitor is? § In pic § The power delivered by the battery and dissipated by the resistor are also at their? § And no energy initially stored by the capacitor bc the stored charge is? § In pic § o After a long time, when time is basically = to infinity, we see that there is? § In pic o Can also use time dependent expressions to calculate current through the circuit and charge on the capacitor at any other point in time -> Ex: calculate current and charge when time is = to RC § Product of RC -> called the RC time constant of the circuit and is a measure of how long it takes the capacitor to charge or discharge § When t = RC -> in pic § Summary in pic
· Consider the set up in pic -> what happens when the switch is closed? -> in pic o Begin by calculating the initial current in the circuit and charge on the capacitor when switch is closed at t=0. § According to expressions for charging capacitor, at t=0, the current is = to its maximum value of the EMF divided by the resistance § Charge on capacitor is = 0 §In pic § The power delivered by the battery and dissipated by the resistor are also at their maximum values § And no energy initially stored by the capacitor bc the stored charge is = 0 § In pic § o After a long time, when time is basically = to infinity, we see that there is no longer any current in the circuit, but charge on capacitor has reached its max value, and the energy stored by the capacitor has also reached its max value § In pic o Can also use time dependent expressions to calculate current through the circuit and charge on the capacitor at any other point in time -> Ex: calculate current and charge when time is = to RC § Product of RC -> called the RC time constant of the circuit and is a measure of how long it takes the capacitor to charge or discharge § When t = RC -> in pic § Summary in pic
· Example -> want to run enough current though piece of copper wire so it floats in mid air (effect called magnetic levitation) -> in pic o Carefully arrange some magnets to create a B field o Question in pic · · · Answer and explain?
· Example -> want to run enough current though piece of copper wire so it floats in mid air (effect called magnetic levitation) -> in pic o Carefully arrange some magnets to create a B field o Question in pic · · · Answer o Since gravitational force on wire (mg) is downward -> we want magnetic field on wire to point upward o Current as shown in pic -> results in upward magnetic force o For wire to levitate -> magntidue of magnetic force on some length of wire must equal its weight -> in pic § Current and magnetic field are perpendicular -> sinø =1 (ø=90˚) o Find mass density of copper -> can calculate the mass of some length of wire from its density and volume § In pic o Write cross sectional area in terms of wires radius -> in pic § Length of wire cancels out! o Solve for current in wire § Logical answer § Levitating something like magnetic train would be much trickier -> special magnets and wires capable of sustaining extremely high currents are required § In pic
· Have seen that faradays law explains how a? · Will modify amperes law to explain how a? · Changing E (electric) and B fields? o Electromagnetic wave? · Light is one example of an? o But EM waves can have? § Gamma rays -> wavelengths of 10^-13 m or smaller § X rays § Visible light -> wavelengths around 10^-7 m § Microwaves § Radio waves -> used (for ex) in cell phone communication -> with wavelengths of 1000 m or more · Topics to be covered?
· Have seen that faradays law explains how a changing magnetic flux can create or induce an electric field (change in magnetic flux -> emf induced -> E field created! -> current induced) · Will modify amperes law to explain how a change in electric flux can create a change in B field · Changing E (electric) and B fields -> can create an electromagnetic wave o Electromagnetic wave -> continuously oscillating E and B field that propagates through space at the speed of light · Light is one example of an electromagnetic (EM) wave o But EM waves can have any wavelength § Gamma rays -> wavelengths of 10^-13 m or smaller § X rays § Visible light -> wavelengths around 10^-7 m § Microwaves § Radio waves -> used (for ex) in cell phone communication -> with wavelengths of 1000 m or more · Topics to be covered o Be able to define an electromagnetic (EM) wave o Discuss how speed, frequency, and wavelength are related for EM waves o Describe properties of an EM wave o Explain what maxwells equations tell us about EM waves o Calculate energy density and intensity (power / area) of EM waves
· A current carrying wire contains moving charges -> as a result? · Startin with expression for magnetic force on charged particles, we know that charged particles move down the wire with a speed = to Vd (drift speed) o Allows us to calculate the B force (magnetic force) on a single charge of magnitude e moving down the wire o How many moving charges does the wire contain § If wire has n charges carries / unit volume -> we can calculate the number of moving charges in some length of a wire with cross-sectional area A o In pic · Can write an expression for total magnetic force acting on the length of wire -> in pic o Recall equation for current in wire -> in pic o In pic o Write magnetic force on length of current carrying wire in pic · Calculate the direction of the magnetic force on the length of wire, by again using? o The velocity of the charged particles is in the direction of the? o Magnetic force on this segment of current carrying wire is again? o In pic
· A current carrying wire contains moving charges -> as a result, these wires can experience a magnetic force when in the presence of a magnetic field (magnetic field acts on charges and thus also affects the wire itself...) · Startin with expression for magnetic force on charged particles, we know that charged particles move down the wire with a speed = to Vd (drift speed) o Allows us to calculate the B force (magnetic force) on a single charge of magnitude e moving down the wire o How many moving charges does the wire contain § If wire has n charges carries / unit volume -> we can calculate the number of moving charges in some length of a wire with cross-sectional area A o In pic Cann write an expression for total magnetic force acting on the length of wire -> in pic o Recall equation for current in wire -> in pic o In pic o Write magnetic force on length of current carrying wire in pic · Calculate the direction of the magnetic force on the length of wire, by again using the right hand rule o The velocity of the charged particles is in the direction of the current through the wire (point fingers in direction of current...flow of + charge) o Magnetic force on this segment of current carrying wire is again parallel to the direction your thumb is facing o In pic
· Alternating current? o Household electric energy -> typically delivered using? Use faradays law to understand? · Coil of wire in a uniform B field oriented at angle ø, we can write the magnetic flux through one turn of the coil o If N turns -> total flux through coil is the flux through one turn multiplied by the number of turns o If relative angle of the coil and the B field changes -> with angular frequency omega? § Such an angular dependence can be created (for ex) by? · Compare this equation to simple harmonic motion equations! -> can write the? · According to faradays law -> the magnitude of the rate of change of the magnetic flux must be? · Important equation! · If coil has resistance (R) -> we can? o Can also calculate? · Even tho emf and current alternate bw + and negative -> the power delivered is? LOTS OF EQUATIONS FROM THIS VIDEO!
· Alternating current -> current that changes direction sinusoidally with time o Household electric energy -> typically delivered using alternating current · Use faradays law to understand generation of alternating current · Coil of wire in a uniform B field oriented at angle ø, we can write the magnetic flux through one turn of the coil o If N turns -> total flux through coil is the flux through one turn multiplied by the number of turns o If relative angle of the coil and the B field changes -> with angular frequency omega, then the magnetic flux will also change with time § Such an angular dependence can be created (for ex) by water or wind turning a turbin in an applied B field · Compare this equation to simple harmonic motion equations! -> can write the time rates of change of magnetic flux through coil · According to faradays law -> the magnitude of the rate of change of the magnetic flux must be the magnitude of the induced emf in the coil · Important equation! · If coil has resistance (R) -> we can calculate the induced current in the coil o Can also calculate the power delivered by this generator · Even tho emf and current alternate bw + and negative -> the power delivered is always +
· Apply ideas of current, voltage, and resistance to circuits that may contain multiple batteries and resistors. o Main tool for this analysis is Kirchoff's rules? § Kirchoffs junction rule -> conservation of? § Kirchoofs loop rule -> conservation of? · We can create series and parallel arrangements of resistors (similar to what we could do with capacitors) in pic · Electric power? o Rate at which? o Depends on the? · RC Circuits o Circuits that contain? o When capacitors are present in a circuit? · Topics to be coverd?
· Apply ideas of current, voltage, and resistance to circuits that may contain multiple batteries and resistors. o Main tool for this analysis is Kirchoff's rules -> math statements of conservation of charge and energy applied to electric circuits § Kirchoffs junction rule -> conservation of charge § Kirchoofs loop rule -> conservation of energy · We can create series and parallel arrangements of resistors (similar to what we could do with capacitors) in pic · Electric power -> rate of energy delivered or used o Rate at which energy is delivered to a circuit or used by an electrical device oDepends on the current through the circuit element and the voltage drop ax that element In pic · RC Circuits o Circuits that contain both resistors and capacitors o When capacitors are present in a circuit -> the current (i) changes with time as the capacitor either discharge or get charged up · Topics to be covered o Current, voltage, and resistance relationships o Kirchoff's loop and juncrtion rules o Combining series in series and parallel arrangements o Electric power delivered or used by an electrical device o RC circuits and behavior
· Apply kirchoffs loop rule -> ex has more than 1 loop o + charge experiences voltage gain as it passes battery from? § + charge experieces voltage loss as it crosses battery from? o + charge experiences voltage drop as it crosses the resistor? § + charge experiences voltage gain as it crosses the resistor in? o Loop with r1 and r2 equations -> in pic (they are different equations) § In pic § Set 2 equations = to each other and see that resistors in parallel have the same voltage drop across them (emf cancels out in the equations!) -> in pic o Could have obtained same result by considering the loop that contained only the 2 resistors § In this case ex? o Use rules in pic? § Replace quantity in parenthesis with one over Requiv (equivalent resistance... sum of resistances...) -> the expression describes a circuit with the same current and emf but? o This general relationship bw the Requiv and an array of parallel resistors can be extended to? § Bc of reciprocal relationship -> the Requiv of an array of parallel resisotrs is always less than? o Resistors in parallel main points? MAJOR FEATURES OF RESISTORS IN PARALLEL?
· Apply kirchoffs loop rule -> ex has more than 1 loop o + charge experiences voltage gain as it passes battery from - terminal to + terminal of battery § + charge experieces voltage loss as it crosses battery from + to - end o + charge experiences voltage drop as it crosses the resistor in direction of the current § + charge experiences voltage gain as it crosses the resistor in opposite direction of the current o Loop with r1 and r2 equations -> in pic (they are different equations) § In pic § Set 2 equations = to each other and see that resistors in parallel have the same voltage drop across them (emf cancels out in the equations!) -> in pic o Could have obtained same result by considering the loop that contained only the 2 resistors § In this case + charge would experience a voltage drop as it crosses R1 in the direction of the current, but to complete loop 2 the + charge would have the cross R2 opposite direction of the current (charge would experience voltage gain as it crosses R2) -> in pic. o Use loop rules to solve for current through each resistor and then apply the junction rule to write the total current as a function of the emf and resistances-> in pic § Replace quantity in parenthesis with one over Requiv (equivalent resistance... sum of resistances...) -> the expression describes a circuit with the same current and emf but with the array of parallel resistors replaced by a single equivalent resistor -> this general relationship bw an equivalent resistance and an array of parallel resistors -> in pic o This general relationship bw the Requiv and an array of parallel resistors can be extended to any number of parallel resistors § Bc of reciprocal relationship -> the Requiv of an array of parallel resisotrs is always less than the smallest resistance of the parallel resistors -> in pic o Resistors in parallel § 1/Requiv = 1/R1 + 1/R2 + 1/R3 +/.... § Voltage applied to resistors is the same! § Current is not constant and changes! MAJOR FEATURES OF RESISTORS IN PARALLEL Parallel resistance is found from 1/𝑅p=1/𝑅1+1/𝑅2+1/𝑅3+... and it is smaller than any individual resistance in the combination. Each resistor in parallel has the same full voltage of the source applied to it. (Power distribution systems most often use parallel connections to supply the myriad devices served with the same voltage and to allow them to operate independently.) Parallel resistors do not each get the total current; they divide it.
· Apply our results for the magnetic force on a current carrying wire to a current carrying loop bent in the shape of a rectangle and placed in a uniform magnetic field (bent into the screen in this ex) o X's -> magnetic field going? o Dots -> magnetic field going? · Examine force on each segment separately -> walk through ex? o Net magnetic force on a closed rectangular current carrying loop in a uniform magnetic field? o This calculation was for a rectangular loop for given orientation § BUT result is completely? § Net magnetic force on any current carrying loop in uniform magnetic field? In pic
· Apply our results for the magnetic force on a current carrying wire to a current carrying loop bent in the shape of a rectangle and placed in a uniform magnetic field (bent into the screen in this ex) o X's -> magnetic field going into the plane (Screen) o Dots -> magnetic field going out of the plane (screen) · Examine force on each segment separately o Start with 1-2 § Current is right and magnetic field is into screen -> 90˚angle bw the two and sin90 = 1 § Right hand rule (rhr) -> direction of the force on this wire segment is direction straight up (fingers in direction of current and palm facing the magnetic field direction -> thumb is direction of magnetic force) o 3-4 § Same length as 1-2 and carries the same current but direction is to the left § Force on this segment is same magnitude as 1-2 but is directed downward (rhr) o F12 + F34 = 0 (the forces cancel out!) § Apply similar argument to left and right side of the rectangle; F14 + F23 = 0 (forces cancel) o Net magnetic force on a closed rectangular current carrying loop in a uniform magnetic field = 0 o This calculation was for a rectangular loop for given orientation § BUT result is completely general for any current carrying loop with any orientation or any shape relative to a uniform mangetic field § Net magnetic force on any current carrying loop in uniform magnetic field= 0 In pic
· Battery and some electric device (ex: lightbulb) are attached with wires, the potential difference (voltage) bw the ends of the battery creates and? o As result -> electrons flow from where to where? § + charge flows in the? § In pic o When analyzing circuits -> we almost always talk about the flow of? § Current is the direction of? · Why? o In biological systems -> both + and - charged ions can serve as? o If we measure one point of the circuit and measure how much charge flow has passed that point in a certain interval of time we can calculate the? § Current is rate at which? § In pic o Unit of current (i) is? § Common household current usually ranges up to? § Current in small electronic devices can be measured in? § Current -> direction of? § Current is not a? why? § In pic §In pic
· Battery and some electric device (ex: lightbulb) are attached with wires, the potential difference (voltage) bw the ends of the battery creates and E (electric field) in the wires and bulb of the circuit o As result -> electrons flow from - end of battery, through the wires and bulb,and into the + end of the battery § + charge flows in the opposite direction; from the + end of battery, through the circuit and into the - end of the battery § In pic o When analyzing circuits -> we almost always talk about the flow of + charge even tho we know that it is really - charged electrons in the circuit that are moving, not + charged protons § Current is the direction of + charge flow! · Why? -> by convention, often attributed to Ben Franklin; the fact that it was - charged elecrtrons that actually move in circuits wasn't discovered until many years after his death at which point the convention was too well established to change o In biological systems -> both + and - charged ions can serve as the source of current o If we measure one point of the circuit and measure how much charge flow has passed that point in a certain interval of time we can calculate the current (I) in the circuit § Current is rate at which charge flows -> i (dividing charge measured by time) § In pic o Unit of current (i) is C/second = Ampere (amp for short) -> A § Common household current usually ranges up to about 15 amps § Current in small electronic devices can be measured in milliamps or microamps or even less § Current -> direction of + charge flow, is in a given direction around a circuit § Current is not a vector quantity -> bc at different points in the circuit, charges might be flowing down, up, right, or left -> no single direction we can use to identify the direction of the currents at all points in the circuit § In pic § In pic
· Because magnetic force acts perpendicular to the velocity of a charged particle -> resulting motion of the particle will have a? o Consider a + charged particle directed upward and entering region of uniform magnetic field directed out of screen (represented by dots) § explain ex? § In pic § In pic · This can be used to create a? o If ions with a known velocity are shot into a region of known uniform magnetic field they will travel a? § If detector is placed, then? § Assume particles are singularly ionized -> mass of particles can be determined § In pic o Ex in pic § Each molecular ion will hit the detector a distance of? § Given parameters are reasonable § Quite a sensitive instrument for differentiating bw isotopes (as distance of 2.6 cm should be easily measurable) · In pic
· Because magnetic force acts perpendicular to the velocity of a charged particle -> resulting motion of the particle will have a circular component o Consider a + charged particle directed upward and entering region of uniform magnetic field directed out of screen (represented by dots) § Force on particle -> initially directed to the right and causes an acceleration in this direction § At later point -> force will be directed down and to the right and so on as particle moves on a circular parth o Applying netwon 2nd law using magnetic force on the particle and recognizing that the acceleration points in the centripetal direction -> can solve for for the raidus of the charged particles motion § In this ex -> velocity is perpendicular to the magnetic field -> sinø=1 § In pic § In pic · This can be used to create a mass spectrometer -> device used to determine masses of individual atoms and molecules o If ions with a known velocity are shot into a region of known uniform magnetic field they will travel a circular path § If detector is placed, then diameter of the circular path can be measured § Assume particles are singularly ionized -> mass of particles can be determined § In pic o Ex in pic § Each molecular ion will hit the detector a distance of one diameter (2r) from the entry point § Given parameters are reasonable § Quite a sensitive instrument for differentiating bw isotopes (as distance of 2.6 cm should be easily measurable) · In pic
· Calculate net electric field due to distribution of electric charges? o In pic · To calculate the magnetic field due to a long straight wire o Split wire up into? o Present result of this calculation and use it to motivate? · Magnetic field of a very long current carrying wire is proportional to? o Constant in pic? · To calculate direction of the magnetic field (around wire) -> invoke? o how? o In pic · Magnetic field lines of a long straight wire are? o Magnitude of the B field is? o Move farther from wire? o In pic
· Calculate net electric field due to distribution of electric charges -> add together electric fields from each individual charge o In pic · To calculate the magnetic field due to a long straight wire o Split wire up into very small length segments and calculate the magnetic field vector at a particular point due to each segment and add individual magnetic fields together to arrive at the magnetic field at that point -> in pic -> requires use of calculus (beyond scope of course) o Present result of this calculation and use it to motivate ampere's law (different approach to calculating magnetic fields) -> in pic · Magnetic field of a very long current carrying wire is proportional to the current in the wire and inversely proportional to the distance from the wire o Constant in pic -> permeability of free space (represents magnetic properties of vacuum)-> in pic · To calculate direction of the magnetic field (around wire) -> invoke second rhr (right hand rule) o Point thumb in direction of current -> fingers wrap in direction of magnetic field o In pic · Magnetic field lines of a long straight wire are circles centered on the wire o Magnitude of the B field is same everywhere on the circle o Move farther from wire -> circulating magnetic field lines are separated by greater distances bc magnetic field is decreasing in magnitude o In pic
Prelecture 6a · Can take advantage of current of moving charges to power? · When charges move in a magnetic field, they may experience? o Magnetic force -> only non-friction like force that is exerted only on? oIn pic · Electric and magnetic forces are different manifestations of the same? o Will treat electric and magnetic forces separately for now tho · You have likely taken advantage of magnetic forces by using a compass needle to tell you which direction you are facing or sticking art to fridge with magnets o Some magnetic switches called soloids -> also make use of magnetic forces · Topics to be covered?
· Can take advantage of current of moving charges to power electric circuit · When charges move in a magnetic field, they may experience magnetic forces o Magnetic force -> only non-friction like force that is exerted only on moving objects (doesn't act on static charges!) o In pic · Electric and magnetic forces are different manifestations of the same fundamental electromagnetic force o Will treat electric and magnetic forces separately for now tho · You have likely taken advantage of magnetic forces by using a compass needle to tell you which direction you are facing or sticking art to fridge with magnets o Some magnetic switches called soloids -> also make use of magnetic forces · Topics to be covered o Properties of magnetic force § Like electric force -> magnetic force can act over long distances o Magnetic forces on charged particles § Calculated magnitude and direction o Magnetic forces on current carrying wires § Calculated magnitude and direction o Mass spectrometer § Apply magnetic force to understand how mass spectrometer works
· Charged particles in magnetic fields (revealed by experiements) o If a charged particle in a magnetic field is not moving? § In pic o If a charged particle moves in a direction parallel to or opposite to the direction of the magnetic field? § In pic (could be moving up or down in pic... must be parallel tho) o Charged particles feel the largest magnitude of (magnetic) force when they move in a direction? § Force exerted on the charged particle is perpendicular to both? §In pic (think circular motion too...) o If the velocity of the charged particle reverses? §In pic o If the direction of the magnetic field reverses? §In pic o If the sign of the charge changes ? §In pic o Magntidue of magnetic force is proportional to? § In pic
· Charged particles in magnetic fields (revealed by experiements) o If a charged particle in a magnetic field is not moving -> charge experiences no magnetic force §In pic o If a charged particle moves in a direction parallel to or opposite to the direction of the magnetic field -> charge experiences no magnetic force §In pic (could be moving up or down in pic... must be parallel tho) o Charged particles feel the largest magnitude of (magnetic) force when they move in a direction perpendicular to the magnetic field lines § Force exerted on the charged particle is perpendicular to both the velocity of the charged particle and the direction of the magnetic field § In pic (think circular motion too...) o If the velocity of the charged particle reverses -> then the (magnetic) force exerted on it also reverses § In pic o If the direction of the magnetic field reverses, then the force exerted on the charged particle also reverses (right hand rule... in book!) § In pic o If the sign of the charge changes -> the direction of the force reverses § In pic o Magntidue of magnetic force is proportional to the magnitude of the charge on the charged particle, the speed of the particle, and the magnitude of the magnetic field § In pic
· Consider a circuit with more than 1 loop o Junctions? o Resistors are in parallel because current can? o There are a fixed number of? § Ex: so every charge that enters point A? · Some charges go through R1 and others through R2 o Kirchoff's junction rule? § Ex? o In pic
· Consider a circuit with more than 1 loop o Junctions -> points where the current either splits or recombines (A and B in pic) o Resistors are in parallel because current can traverse both resistors simultaneously o There are a fixed number of charges in the circuit -> they cannot be created or destroyed! And there is no reason for the charges to pile up in a particular location § Ex: so every charge that enters point A must leave through point B (current flows how + charge would) · Some charges go through R1 and others through R2 o Kirchoff's junction rule -> statement of the conservation of charge -> sum of currents into a junction equals the sum of the currents out of a junction § Ex: at A -> i = i1 + i2 § Ex: at B -> i1 + i2 = i o In pic
· Consider a simple circuit with just a battery (sometimes call a source of emf, labeled with script letter E.. in pic) and an electric device like a lightbulb (can model as resistor) o In pic o Emf -> pushes what through what? units? § Current flows out of? § Bc the electric force (which drives charges around the circuit) is a conservative force -> the total change in electric potential energy of a single charge as it makes a complete loop around the circuit must be? § Change in potential is change in? leads to? Kirchoffs loop rule? o Apply kirchoffs loop rule to a simple circuit example (charge moving around loop to the left) -> think through?
· Consider a simple circuit with just a battery (sometimes call a source of emf, labeled with script letter E.. in pic) and an electric device like a lightbulb (can model as resistor) o In pic o Emf -> pushes charges through a circuit and has units of volts § Current flows out of + end of battery (larger line in pic) § Bc the electric force (which drives charges around the circuit) is a conservative force -> the total change in electric potential energy of a single charge as it makes a complete loop around the circuit must be 0 § Change in potential is change in electric PE / unit charge -> leads us to Kirchoff's loop rule (Statement of conservation of energy) Kirchoffs loop rule -> sum of changes in electric potential around a closed loop in a circuit must equal 0. -> in pic o Apply kirchoffs loop rule to a simple circuit example (charge moving around loop to the left) § Follow + charge around the circuit starting at point A (assuming wires have no resistance) § As charge travels along the wire -> experiences no change in voltage as start · When charge encounters the battry -> electric potential of charge increases bc charge is traveling from - to + end of battery · Electric potential remains constant at new value until it encounters the resistor -> our + charge crosses the resistor in the direction of the current so voltage is reduced by amount given by ohms law · Since there are no other places where the electric potential can change -> the voltage drop ax this one resistor must equal the voltage gain ax the battery · Charge continues on way until it returns to point A · If emf and resistance are known then expression in pic could be used to solve for current in circuit · In pic
Prelecture 6b · Continue study of magnetic forces and explore source of magnetic fields · If current carrying wire is shaped into a loop o Net magnetic force on loop is? o Magnetic torque? § Magnetic torque -> basis for all? · Source of magnetic fields o All magnetic fields originate from the? o In certain situations -> learn to calculate the? · Topics to be covered o Calculate the net magnetic force from an external uniform magnetic field on a current carrying loop of fire o Calculate the magnetic torque from an external uniform magnetic field on a current carrying loop of wire and explain when this torque appears and the resultant rotation of the wire o Explain how moving electric charges creates magnetic fields o Use ampere's law to calculate the magnetic fields due to currents in some wire geometries (Such as long, straight wires and solenoids) o In pic
· Continue study of magnetic forces and explore source of magnetic fields · If current carrying wire is shaped into a loop o Net magnetic force on loop is zero o Magnetic torque is exerted on the loop -> causing it to rotate § Magnetic torque -> basis for all electric motors -> in pic · Source of magnetic fields o All magnetic fields originate from the motion of electric charges o In certain situations -> learn to calculate the magnetic field created by those moving moving charges, using amperes law (one of the equations that eventually became known as maxwell's equations) · Topics to be covered o Calculate the net magnetic force from an external uniform magnetic field on a current carrying loop of fire o Calculate the magnetic torque from an external uniform magnetic field on a current carrying loop of wire and explain when this torque appears and the resultant rotation of the wire o Explain how moving electric charges creates magnetic fields o Use ampere's law to calculate the magnetic fields due to currents in some wire geometries (Such as long, straight wires and solenoids) o In pic
· EM waves propagate through vacuums at? o As with all waves -> speed, frq (frequency), and wavelength of wave are? o Since we always know speed of wave in vacuum, if we know the frq or the wavelength? · If wave travels in medium other than a vacuum -> speed of wave is? o Ex? o Speed of wave through medium also depends on ? · EM waves are? o Magnitude of the electric (E) and magnetic (B) fields oscillate in directions? o Representation of sinusoidal plane wave § At any instant -> the E and B fields each have a? o Both E and B fields of a plane wave can be described using? § E and B field magnitudes are related by? o Important characterizes of EM waves -> like mechanical waves, EM waves transfer? o Have described many properties of EM waves -> will see how?
· EM waves propagate through vacuums at the speed of light (constant) o As with all waves -> speed, frq (frequency), and wavelength of wave are related for EM waves o Since we always know speed of wave in vacuum, if we know the frq or the wavelength -> the other is easy to calculate · If wave travels in medium other than a vacuum -> speed of wave is reduced o Ex: reduced speed of light through glass -> explains how lens work o Speed of wave through medium also depends on frq of wave -> Explains the formation of a spectrum of colors when white light shines on a prism · EM waves are transverse waves o Magnitude of the electric (E) and magnetic (B) fields oscillate in directions perpendicular to the direction that the wave propagates and the perpendicular to to each other -> this oscillation creates the EM wave o Representation of sinusoidal plane wave § At any instant -> the E and B fields each have a uniform magnitude and direction everywhere on a plane drawn perpendicular to the direction the wave travels o Both E and B fields of a plane wave can be described using cos functions § E and B field magnitudes are related by speed of light (C) o Important characterizes of EM waves -> like mechanical waves, EM waves transfer energy from one location to another without any physical objects actually moving from the source location to the destination o Have described many properties of EM waves -> will see how these properties are a direct result of maxwell's equations!
Physics 104 Prelecture 4a · Electrostatics? · Electric forces can cause charges to ? · Will study charges what? create? o Current can be used to? oIn pic · By end of prelecture -> should be able to?
· Electrostatics -> study of charges that are in static equilibrium (Where are discussion of electric forces has mostly been this far) -> ex: those charges stored in a capacitor · Electric forces can cause charges to accelerate, but what happens then? · Will study charges in motion -> which create an electric current o Current can be used to run electric devices, power mobile electric devices, and direct electric systems throughout the nervous system (sensory signal to brain to process and from brain to control physical motion) o In pic · By end of prelecture -> should be able to o Explain why moving charges are important o Relate current and drift speed o Use relationship among current, voltage, resistance, and resistivty to describe characteristics of a simple circuit o Simple circuit
· Ex: loop by magnet and move the magnet o Induced current is present while? o Stationary magnet? o Not due to? § Changing magnetic field? · Both induced emf and motional emf -> can be described by? o Gauss's law? o define magnetic flux as? §Magnetic flux of loop will change if? · Combine observations with defn of magnetic flux -> any emf (motional or induced) is created only when? oMagnitude induced emf is = to? · Important equations!
· Ex: loop by magnet and move the magnet o Induced current is present while magnet is moved toward the loop (current reverse direction when magnetic is moved in opposite direction) o Stationary magnet -> no current is induced o Not due to motional emf and B force on charges! Bc wire (loop) and thus charges have no v (velocity) -> no B force! § Changing magnetic field -> creates induced emf in circuit -> exerts electric (E) force on charges in the loop -> induced current in the loop · Both induced emf and motional emf -> can be described by considering the magnetic flux through the conducting loop o Gauss's law -> described electric flux as the component of the E field perpendicular to an area multipled by the area o define magnetic flux as the component of the B field perpendicular to an area, multiplied by the area § Magnetic flux of loop will change if the area of the loop changes, the magnitude of the B field changes, or the angle of the magnetic field relative to the loop changes · Combine observations with defn of magnetic flux -> any emf (motional or induced) is created only when the magnetic flux is changing o Magnitude induced emf is = to rate at which magnetic flux through loop changes (Faradays law) · Important equations!
· Ex: round loop of wire with current of 100A and r of 10cm and B field of 0.244T and ø=30˚?? o In pic -> explain? o As orientation of the loop changes § As plane of loop approaches being perpendicular to the B field? § As plane of loop becomes parallel to the magnetic field? § In pic
· Ex: round loop of wire with current of 100A and r of 10cm and B field of 0.244T and ø=30˚?? o In pic o be careful with the sinø(angle between side of loop and B field as shown in pic) § Plane of loop perpendicular to the B field -> ø=0˚ for torque § Plane of loop parallel to B field -> ø=90˚ for torque § As we rotate loop so that plane of loop makes a 30˚ with the B field -> see that angle we need to use to calculate the torque is 90˚ - 30˚ = 60˚ In pic oCalculate torque on loop -> in pic o As orientation of the loop changes § As plane of loop approaches being perpendicular to the B field -> angle used in calculating torque approaches 0 so sin0=0 and torque = 0 § As plane of loop becomes parallel to the magnetic field -> angle used in calculating torque approaches 90˚ -> sin90=1 and torque approaches max § In pic
Prelecture 7a · Have explored E (electric) fields and force and B (magnetic) fields and forces as? · Will explore? ·When a B field changes? · Electromagnetic induction (many applications)? · By end of prelecture?
· Have explored E (electric) fields and force and B (magnetic) fields and forces as separate phenomena · Will explore electromagnetic induction -> links E and B fields · When a B field changes -> it creates (or induces) an E field (B field changes -> makes emf -> makes E field which induces current ) · Electromagnetic induction (many applications)-> underlying principle behind transcranial magnetic stimulation o Nearly every form of electric power induction -> relies on electromagnetic induction · By end of prelecture o Explain importance of electromagnetic induction o Describe differences bw motional emf and induced emf o Explain how to determine magnitude and direction of induced emf in an electric circuit o Define key properties of an AC generator
· I (current) tells use the rate at which? o Doesn't tell us how fast the? · Drift speed (Vd)? o Closely related to? o In pic (Vdrift and I are in the same direction!) o In circuit -> - charge electrons move along the? § If a - charge moves left to right along a wire> same result as? · Doesn't really matter which sign of charge? ·In pic · Piece of copper for ex -> consider small length of copper wire o Has certain number of free electrons per unit? § Since we can talk about + or - charges -> pretend that mobile charges each actually have a? o Cross sectional area (A) o In pic · Total charge on all charge carriers (total charge in wire segment) -> in pic o In pic o All of the charges will drift down the length of the wire at some? can calculate? o Current is then = to? o In pic o in pic
· I (current) tells use the rate at which charge passes a particular point in a circuit o Doesn't tell us how fast the individually charged particles actually pass that point · Drift speed (Vd) -> net speed at which particles travel down a wire o Closely related to current o In pic (Vdrift and I are in the same direction!) o In circuit -> - charge electrons move along the wire § If a - charge moves left to right along a wire -> resulting left in left side of wire being more + and right end of wire being more - (negative) -> this is the same result we would get if a + charge of = magnitude moved from right to left -> electrically equivalent · Doesn't really matter which sign of charge is actually moving -> we can easily talk about current and the motion of + charges even if they don't really exist · In pic · Piece of copper for ex -> consider small length of copper wire o Has certain number of free electrons per unit volume (n -> number density of charged particles) § Since we can talk about + or - charges -> pretend that mobile charges each actually have a + charge = to the magnitude of the charge on an electron (-) o Cross sectional area (A) o In pic · Total charge on all charge carriers (total charge in wire segment) -> in pic o In pic o All of the charges will drift down the length of the wire at some speed -> we can calculate the total time it takes for all the charges originally in that volume of wire to leave o Current is then = to the total charge / time it takes that charge to leave o In pic o In pic
· INSTRUCTOR: How do the individual charges that make up current in a wire create the field pattern you saw on the previous slide? o An individual charge creates a magnetic field that points in space as it moves by-- as shown here?? § In pic (circle is arbirary point to measure B field...) o The field lines created by a single moving charge look like this? § In pic ·If many individual charges are moving together? o In pic
· INSTRUCTOR: How do the individual charges that make up current in a wire create the field pattern you saw on the previous slide? o An individual charge creates a magnetic field that points in space as it moves by-- as shown here. § In pic (circle is arbirary point to measure B field...) o The field lines created by a single moving charge look like this. § In pic · If many individual charges are moving together, their fields will add up to something that looks like the field created by a current carrying wire through superposition. o In pic
· INSTRUCTOR: Maxwell's equations are? . A few of these symbols or names might be familiar. We've already covered some of the foundations of Maxwell's equations. Rather than delve deeper into specifics, suffice it to say that the upshot of these four expressions is that? It is this mutual creation that? · When a charge experiences a change in motion-- that is, an acceleration-- it creates? Note that these kinks are largest perpendicular? If a charge oscillates back and forth, the frequency of that oscillation is the same as? · The changing electric field around the accelerating charge will induce a? . We've already seen that the reverse happens as well, that the changing magnetic field around the charge will induce a? These two fields continue to? · When an electromagnetic wave encounters a material, the charges in that material can respond? explain each? · The way a material responds to incoming electromagnetic waves can vary with the? A material might transmit some frequencies but? · Molecules, like any other system, can have? . If you drive them at this frequency,? o The image shows carbon dioxide's response to an external electric field, the blue arrow, and how that response is larger when the field oscillates at just the right rate · If we apply an alternating voltage to a conductor, like a tall metal pole-- that is, an antenna-- we can get charges to? · By choosing the frequency of the alternating voltage, we can adjust the frequency? Charges in nearby conductors can respond to? allowing us to? ·flow of EM wave formation?
· INSTRUCTOR: Maxwell's equations are a combination of four expressions that together give us insight into the nature of electromagnetic waves. A few of these symbols or names might be familiar. We've already covered some of the foundations of Maxwell's equations. Rather than delve deeper into specifics, suffice it to say that the upshot of these four expressions is that changing electric fields induce changing magnetic fields, and changing magnetic fields induce changing electric fields. · It is this mutual creation that allows electromagnetic waves to exist and propagate. · When a charge experiences a change in motion-- that is, an acceleration-- it creates kinks in the electric field to propagate outward at the speed of light. Note that these kinks are largest perpendicular to the charges direction of motion. If a charge oscillates back and forth, the frequency of that oscillation is the same as the frequency of the changes in the electric field. · The changing electric field around the accelerating charge will induce a changing magnetic field. We've already seen that the reverse happens as well, that the changing magnetic field around the charge will induce a changing electric field. These two fields continue to create and sustain one another as they move out into space. Such self-sustaining oscillations of electric and magnetic fields, which you now know to call electromagnetic waves, can travel enormous distances, e fields creating b fields an d b fields creating e fields. · When an electromagnetic wave encounters a material, the charges in that material can respond in a number of ways that produce a number of effects. If the charges in the material oscillate in the right way and emit their own electromagnetic waves, the wave can be reflected outward. If the charges don't respond to the electromagnetic fields of the wave, it can pass through the material. o The charges can also move in response to the e and b fields but convert this motion into heat energy. In this case, the original electromagnetic wave is absorbed. · The way a material responds to incoming electromagnetic waves can vary with the frequency and wavelength of the waves. A material might transmit some frequencies but reflect or absorb others. · Molecules, like any other system, can have resonant frequencies (natural frequency of an object where it tends to vibrate at a higher amplitude??) . If you drive them at this frequency, they will respond strongly. At other frequencies, they won't respond much at all. Carbon dioxide, for instance, has a resonant frequency in the infrared part of the electromagnetic spectrum, a characteristic that makes it a greenhouse gas. o The image shows carbon dioxide's response to an external electric field, the blue arrow, and how that response is larger when the field oscillates at just the right rate · If we apply an alternating voltage to a conductor, like a tall metal pole-- that is, an antenna-- we can get charges to oscillate up and down. · By choosing the frequency of the alternating voltage, we can adjust the frequency of the electromagnetic waves emitted. Charges in nearby conductors can respond to the oscillating electric and magnetic fields in these ways, allowing us to send and receive signals. · Charge oscillates (motion changes -> acceleration) -> E field is kinked -> changing E field is sent out at speed of light-> changing E field induces a changing B field -> changing B field induces(reinforces the already present?) a changing E field -> changing E and B fields sustain each other and create an EM wave!
· In living cells, K ions can flow through K channels in a cell membrane when a? ex problem! o Using patch clamp -> researchers can control the? oEx question and answer -> in pic § Resistance of K channel? · Why is this resistance so large? o One reason? oCalculate E field magnitude required to create that current in pic (treat it like a capacitor!) § Electric field ax membrane is very?
· In living cells, K ions can flow through K channels in a cell membrane when a potential difference is present (would make E field??) -> ex problems! o Using patch clamp -> researchers can control the electrical potential difference (voltage) ax a small patch of membrane and measure the resulting current through individual voltage gated K channels o Ex question and answer -> in pic § Resistance of K channel -> quite high (close to that of some insulating materials) -> but resistance of K channel is less than resistance of rest of membrane (that's why K flows here...) · Why is this resistance so large? o One reason -> K channels are usually only about a nm wide -> means that K ions (K+) must travel single file through the channel -> this is much more restrictive than what happens with metal wires o Calculate E field magnitude required to create that current in pic (treat it like a capacitor!) § Electric field ax membrane is very large -> electric fields this large in the air would result in sparks and electric arcing
· In this prelecture (summary) oContinued are study of circuits -> introducing kirchoffs laws which can be used to analyze a wide range of circuits -> in pic o When resistors are attached in series? § Requiv of resistors in series -> is? § In pic o When resistors are attached in parallel? § In pic o When a circuit contains both a resistor and a capacitor, the current in the circuit and the charge stored on the capacitor? § In pic -> important!
· In this prelecture o Continued are study of circuits -> introducing kirchoffs laws which can be used to analyze a wide range of circuits -> in pic o When resistors are attached in series -> the current through each resistor is the same, and the total voltage across all the resistors is = to the sum of the voltages ax each resistor § Requiv of resistors in series -> is sum of each individual resistance § In pic o When resistors are attached in parallel § Voltage ax each resistor is the same § Total current through array of resistors is = to the sum of the currents through each individual resistor § The reciprocal of the Requiv of resistors attached in parallel is the sum of the reciprocal of the individual resistances § In pic o When a circuit contains both a resistor and a capacitor, the current in the circuit and the charge stored on the capacitor are exponential functions of time § In pic -> important!
· Kirchoffs loop rule -> can be applied to a circuit with? · Ex in pic o + charge crosses resistor in direction of current? § Magnitude of voltage drops depends on? o Sum of the voltage drops ax each resistor must be equal in magnitude to the? § Examing the expression resulting from applying kirchoffs loop rule -> we see that we can factor out the current (Which is same through each resistor in series) -> in pic § Replace the sum of the resistances with a? § As far as battery and currents are concerned, there is no difference bw? § For resistors in series -> current through each resistor (and the current through the equivalent resistance) are the? § In pic o Resistance in series main points? MAJOR FEATURES OF RESISTORS IN SERIES?
· Kirchoffs loop rule -> can be applied to a circuit with any number of resistors attached in series · Ex -> in pic with + charge moving in loop to the right starting from A o + charge crosses resistor in direction of current -> voltage drop occurs (given by ohms law) § Magnitude of voltage drops depends on the resistance at each resistor o Sum of the voltage drops ax each resistor must be equal in magnitude to the total voltage gain provided by the battery § Examing the expression resulting from applying kirchoffs loop rule -> we see that we can factor out the current (Which is same through each resistor in series) -> in pic § Replace the sum of the resistances with a single equivalent resistance § As far as battery and currents are concerned, there is no difference bw the 3 separate resistors or a single resistor with a resistance = to the equivalent resistance § For resistors in series -> current through each resistor (and the current through the equivalent resistance) are the same -> in pic § In pic o Resistance in series § Requiv = R1 + R2 + R3 +... § Current (I) is constant among different resistors § Voltage (∆V) is different among different resistors MAJOR FEATURES OF RESISTORS IN SERIES Series resistances add: 𝑅s=𝑅1+𝑅2+𝑅3+.... The same current flows through each resistor in series. Individual resistors in series do not get the total source voltage, but divide it.
· Magnitude of induced emf around a loop is = to? · Loop brought closer to magnet? o Same loop is brought farther from the magnet ? · What determines direction of induced current? o Lenz's law (deduced from physical observations)? § flow? § Any current creates a B field and thus? o If we have loop of current -> the direction of the B field inside the loop? Magnet and loop move closer together? o Magnetic field created by current induced in the loop? § pointing right thumb in the direction of the B field made by the loop (from induced current) ->? · Loop and magnet are separated (made farther apart)? ·Often put lenz law and faradays law in? · Change in magnetic flux? o Try to basically "cancel out" ?
· Magnitude of induced emf around a loop is = to the rate of change of the magnetic flux through that loop · Loop brought closer to magnet -> increases magnetic flux through loop -> curret is in one direction o Same loop is brought farther from the magnet -> decreases the magnetic flux through loop -> current reverse direction! · What determines direction of induced current? o Lenz's law (deduced from physical observations) -> direction of the B field induced within a conducting loop opposes the change in magnetic flux that created it § Change magnetic flux -> induce emf in loop -> induce current in loop -> current in loop makes a B field that opposes the original change in magnetic flux (B field...?)?? § Any current creates a B field and thus induced current -> creates a B field o If we have loop of current -> the direction of the B field inside the loop can be found with RHR (version of RHR-2?) · Magnet and loop move closer together -> B field strength from the magnet inside the loop is increasing -> increase in magnitude of magnetic flux o Magnetic field created by current induced in the loop must be in opposite direction of the B field of the magnet (must oppose the B field of magnet!)... just in this ex! NOT IN ALL CASES! § pointing right thumb in the direction of the B field made by the loop (from inducec current) -> fingers curl in direction of the induced emf and induced current must be in direction that fingers of your right hand curl (in pic) · Loop and magnet are separated (made farther apart) -> B field from the magnet through the loop decreases -> magnetic flux decreases -> induced B field opposes this change so the induced magnetic field must augment the field from the magnet and point in the same direction as the B field of the magnet; pointing right thumb in directoin of induced B field -> right fingers curl in direction of the induced emf and induced current in the loop... think that you need to fill the empty space of B field that left kind of! · Often put lenz law and faradays law in single eqs (equation) · Change in magnetic flux -> induced emf -> induced current -> induced B field (must oppose direction of the magnetic flux change) o Try to basically "cancel out" the B field movement changes by manipulating induced B field
· Net B force (magnetic force) on any current carrying loop in a uniform magnetic field? o Current carrying loops in uniform magnetic fields are often used in? to? § Net force on the loop? torque on the loop? · View of loop from last slide from the side o Force and torque on loop are 0 in this ex -> in pic o If we rotate the loop -> net B force is 0 but torque becomes? § F12 and F34 will each cause the loop to rotate in clockwise direction -> in pic ·Torque on object about a given axis due to a force is = to? · Calculate torque on current loop about an axis perpendicular to the screen and passing through the middle of the loop -> explain ex? Using results from previous slide for magnitude of forces on each segment -> in pic o Arrive at compact result for the total torque on a current carrying loop in a uniform magnetic field -> in pic o WL = A (area of rectangle) o Generalize result of rectangular loop to loop of any shape by using the appropriate area -> in pic § At ø = 0˚ -> plane of the loop is perpendicular to the magnetic field and torque is? § At ø- 90˚ -> plane of the loop is parallel to the B field and torque is? § Torque is proportional to both? In pic · Summary equation o In pic ->
· Net B force (magnetic force) on any current carrying loop in a uniform magnetic field = 0 o Current carrying loops in uniform magnetic fields are often used in motors to convert electrical energy to mechanical energy § Net force on the loop is 0 but torque on that loop is usually not 0 · View of loop from last slide from the side o Force and torque on loop are 0 in this ex -> in pic o If we rotate the loop -> net B force is 0 but torque becomes non 0 § F12 and F34 will each cause the loop to rotate in clockwise direction -> in pic · Torque on object about a given axis due to a force is = to magnitude of that force multipled by the distance bw where the force is applied and the axis of rotation and sin of angle bw these 2 lines -> in pic · Calculate torque on current loop about an axis perpendicular to the screen and passing through the middle of the loop o Distance of rotation axis to segment 12 is half the length of side we can see o Torque in pic o Direction tends to rotate loop clockwise (in pic) o Similar analysis for 34 side -> use above equation (in pic) o In pic · Using results from previous slide for magnitude of forces on each segment -> in pic o Arrive at compact result for the total torque on a current carrying loop in a uniform magnetic field -> in pic o WL = A (area of rectangle) o Generalize result of rectangular loop to loop of any shape by using the appropriate area -> in pic § At ø = 0˚ -> plane of the loop is perpendicular to the magnetic field and torque is 0 § At ø- 90˚ -> plane of the loop is parallel to the B field and torque is maximum § Torque is proportional to both current and area of loop as well! § In pic · Summary equation o In pic -> think of current coming in and out of plane of page here to find direction of B force!
· Only moving charges experience? o So far -> we have only said that origin of magnetic fields is that they are produced by magnets · Whats happening inside a magnet makes it a magnet? o But we can? · If we run current through coil of wire? o Magnetic field created by these coils? o In pic · Current carrying coil has a? o In pic · 2 current carrying coils? o Conclusion -> motion of elecrtric charges creates? § Breaks down a bit at? o In pic · Location of the magnetic north and south poles depend on the direction of the? o In pic · Turn attention to the details of the magnetic force created by moving charges
· Only moving charges experience magnetic forces o So far -> we have only said that origin of magnetic fields is that they are produced by magnets · Whats happening inside a magnet makes it a magnet -> quite complex answer since the properties of a magnet can only be described using quantum mechanics o But we can learn some things by examing larger scale electric currents · If we run current through coil of wire -> a magnetic field is created o Magnetic field created by these coils looks almost exactly like the magnetic field produced by a bar magnet o In pic · Current carrying coil has a north and a south pole which attract and repel the north and south poles of permanent magnets (acts as if it were a permanent magnet) o In pic · 2 current carrying coils -> attract and repel each other's north and south poles (just as if they were permanent magnets) o Conclusion -> motion of elecrtric charges creates magnetic fields § Breaks down a bit at quantum mechanic level -> model is still helpful tho (even at quantum level...) o In pic · Location of the magnetic north and south poles depend on the direction of the current and the direction that the coils are wound o In pic · Turn attention to the details of the magnetic force created by moving charges
· Permanent magnetic -> object made of? · Magnets can exert magnetic forces on? o In pic o Like electric force -> magnetic force can act at a? o Describe electric forces using idea of? § Describe magnetic forces using idea of? · Relatively easy to visualize? o Small iron filings brought into presence of magnetic field -> align themselves along the magnetic field lines o In pic · Similar to the + and - charges responsible for creating electric fields... o Magnets have what we call a? § Unlike charges, every magnet always has a? § Have not yet been able to observe an? § In pic · Outside of a magnet, the magnetic field lines point? o Unlike electric fields, magnetic field lines do not? § Inside the magnet, the magnetic field lines point from? § In pic (south on left side and north on right side) o Similar to electric charges § Opposite poles of 2 magnets?? § Like poles of 2 magnets? § In pic · Fundamental cause of magnetic fields... in next prelecture we will? o For now, assume we have magnetic fields created by a permanent magnet or some other source and we will focus on what happens when charges move in these magnetic fields
· Permanent magnetic -> object made of one or more of a small number of materials like iron and cobalt · Magnets can exert magnetic forces on other magnets and also on materials that we don't generally think of as magnets oIn pic o Like electric force -> magnetic force can act at a distance o Describe electric forces using idea of electric field § Describe magnetic forces using idea of magnetic field · Relatively easy to visualize magnetic field lines o Small iron filings brought into presence of magnetic field -> align themselves along the magnetic field lines o In pic · Similar to the + and - charges responsible for creating electric fields... o Magnets have what we call a north pole and a south pole § Unlike charges, every magnet always has a north pole and a south pole, even after we break it § Have not yet been able to observe an isolated magnetic pole and thus refer to magnets as magnetic dipoles usually § In pic · Outside of a magnet, the magnetic field lines point away from the north pole and toward the south pole o Unlike electric fields, magnetic field lines do not start and end on the poles § Inside the magnet, the magnetic field lines point from the south pole to the north pole making the magnetic field lines continuous -> thus we often refer to loops of magnetic field! § In pic (south on left side and north on right side) o Similar to electric charges § Opposite poles of 2 magnets attract each other § Like poles of 2 magnets repel § In pic · Fundamental cause of magnetic fields... in next prelecture we will... o We understand magnetic properties to be the result of moving charges o Learn how to calculate the magnetic fields create by currents o In pic o For now, assume we have magnetic fields created by a permanent magnet or some other source and we will focus on what happens when charges move in these magnetic fields
· Power? o Rate? o In pic ·In electric circuits -> batterie deliver? ·Change in electric PE of a small amount of charge (∆Q) depends on? o Rate at which the electric energy is delivered or consumed is then? oEquations in pic (for simplicity ∆V is replaced with V) § Expression is general and valid for any circuit element! -> P = iV that is, P = i∆V · If we now consider resistors recall that we can write the voltage drop in terms of current and resistance or the current in terms of? o power dissipated by a resistor equations -> in pic In pic -> important!
· Power is the rate at which work is done on a system o Rate at which system either delivers or absorbs energy o In pic ·In electric circuits -> batterie deliver power to a circuit and resistors (or devices that can be modeled as resistors) use that electric power, converting it to other useful forms of energy -> in pic ·Change in electric PE of a small amount of charge (∆Q) depends on the amount of charge and the change in voltage that it experiences -> in pic o Rate at which the electric energy is delivered or consumed is then this change in energy divided by the time required for the change to occur o Equations in pic (for simplicity ∆V is replaced with V) § Expression is general and valid for any circuit element! -> P = iV that is, P = i∆V · If we now consider resistors recall that we can write the voltage drop in terms of current and resistance or the current in terms of the voltage drop and resistance o power dissipated by a resistor equations -> in pic · In pic -> important!
· Relationship among the velocity, force, and magnetic field vectors describes on previous slide -> can be written as a cross product · Magnitude of the magnetic force on a moving charged particle o Depends on? § Symbol B used for? § SI unit of magnetic field? § In pic · Direction of the magnetic force can be determined from? osteps? § Your thumb points in the direction of the magnetic force acting on a? · In pic § Your thumb points points in the opposite direction of the magnetic force acting on a? · In pic o Ex?
· Relationship among the velocity, force, and magnetic field vectors describes on previous slide -> can be written as a cross product · Magnitude of the magnetic force on a moving charged particle o Depends on charge, speed of charge, magnitude of magnetic field, and angle bw the velocity of the particle and the magnetic field § Symbol B used for magnetic field § SI unit of magnetic field -> Tesla (T) § In pic · Direction of the magnetic force can be determined from the directions of the velocity and magnetic field vectors using a right hand rule o 1. Point fingers of your right hand in direction of the velocity vector o 2. Rotate your hand until your palm faces toward the magnetic field vector o 3. Curl fingers of right hand toward the magnetic field vector o 4. Stick your thumb out § Your thumb points in the direction of the magnetic force acting on a + charge at that instant in time · In pic § Your thumb points points in the opposite direction of the magnetic force acting on a - charge at that instant in time · In pic o Ex:
· Summary of prelecture o Began study of current? § Charge flowing? § When a voltage is applied ax a voltage, bulb, or other device the resulting? § In pic o Ratio of applied voltage to the current is called the? § If resistance remains constant independent of the applied voltage, this relation is called? § Resistance of chunk of materials depends on its? § In pic
· Summary of prelecture o Began study of current -> net flow of charge in a particular direction § Charge flowing past a given point per unit time § When a voltage is applied ax a voltage, bulb, or other device the resulting E field causes a current through the device § In pic o Ratio of applied voltage to the current is called the resistance of an object (always true...) -> in pic § If resistance remains constant independent of the applied voltage, this relation is called ohm's law (often written as way below) § Resistance of chunk of materials depends on its geometry and the material of which its made § In pic
· Summary of prelecture o Fnet on current carrying loop in uniform magnetic field =?, torque is usually?? § As result -> current carrying loop in a (uniform) B field tends to? § In pic o Moving charges creates? o Ampere's law can help us calculate the? § In pic § In particular the B field created by a long current carrying wire depends on? · Rhr 2 can be used to determine the? o Inside a solenoid?
· Summary of prelecture o Fnet on current carrying loop in uniform magnetic field = 0, torque is usually non 0 § As result -> current carrying loop in a B field tends to rotate § In pic o Moving charges creates magnetic fields -> in pic o Ampere's law can help us calculate the B field of some arrangements of current § In pic § In particular the B field created by a long current carrying wire depends on your distance from the wire · Rhr 2 can be used to determine the direction of the circulation of the B field around the wire -> pic o Inside a solenoid -> B field is constant and directed down the length of the solenoid -> rhr can also be used to determine the direction of the B field created by a solenoid (fingers in direction of current -> thumb points in direction of B field) -> in pic
· Summary slides of this prelecture o Introduced ideas of magnetic fields and magnetic forces o Magnetic forces require a charged particle to be moving with alteast some velocity component perpendicular to the magnetic field § In pic o Calculate magnitude of magnetic force acting on charged particle o Right hand rule -> use to determine direction of magnetic force on charged particle § Because magnetic force is always perpendicular to the direction of the velocity of the charged particle -> Magnetic force always results in centripetal accerlation of the charged particle § In pic o Because current is motion of charged particles -> current carrying wires can also experiences magnetic forces § Right hand rule again used to determine the direction of the magnetic force acting on the wire § In pic Notation -> in pic
· Summary slides of this prelecture o Introduced ideas of magnetic fields and magnetic forces o Magnetic forces require a charged particle to be moving with alteast some velocity component perpendicular to the magnetic field § In pic o Calculate magnitude of magnetic force acting on chaged particle o Right hand rule -> use to determine direction of magnetic force on charged particle § Because magnetic force is always perpendicular to the direction of the velocity of the charged particle -> Magnetic force always results in centripetal accerlation of the charged particle § In pic o Because current is motion of charged particles -> current carrying wires can also experiences magnetic forces § Right hand rule again used to determine the direction of the magnetic force acting on the wire § In pic Notation -> in pic
Question: Two cylindrical resistors are made from the same material. The shorter one has a length 𝐿L and diameter 𝐷D . The longer one has a length 16𝐿16L and diameter 4𝐷4D . How do their resistances compare?
· The resistance of the longer resistor is the same as the resistance of the shorter resistor. o Find R for both -> A of cylinder is pi(r^2) -> use for wires too... o The resistance 𝑅R of each cylindrical resistor is directly proportional to the ratio of the resistor's length 𝐿L to its cross‑sectional area 𝐴A . o 𝑅∝𝐿𝐴R∝LA o The cross-sectional area of a cylinder is proportional to the square of its diameter 𝑑d . 𝐴∝𝑑2A∝d2 o Thus, resistance is proportional to 𝐿L divided by 𝑑2d2 . o 𝑅∝𝐿𝑑2R∝Ld2 · Since the longer resistor has 16 times the length, but also has 16 times the area (i.e., 4 times the diameter), its overall resistance is the same as the shorter resistor. o
Question: Identify the maximum number of unique currents possible for the circuit shown in the figure. -in pic
· Three! -> think i1 leaves and then splits into i2 and i3 at junction and then i2 and i3 recombine to form i1 at next junction! · The circuit diagram depicts two junctions, or nodes, where current can divide or combine. The junctions are located at the points where the vertical branch containing a single resistor in the middle of the circuit connects to the top and bottom of the circuit. The current flowing out of the positive terminal of the battery and through the first resistor divides at the top junction into two currents flowing through the central and right-hand circuit branches. The two currents flowing through the central and right-hand circuit branches recombine at the bottom junction. Thus, there can be three unique currents: the current flowing out of (or into) the battery, the current flowing through the central branch, and the current flowing thorugh the right-hand branch.
· Two parallel long current carrying wires exert? · Consider wire 1 and wire 2 -> each carrying a current from right to left (separated by distance d) explain ex? o Magnetic force bw two parallel wires serves as? § Ampere? o In pic · Currents going in same direction? · Current in opposite directions?
· Two parallel long current carrying wires exert = and opposite magnetic forces on each other · Consider wire 1 and wire 2 -> each carrying a current from right to left (separated by distance d) o Consider magnetic field created by wire 1 at location of wire 2 -> in pic (r is d here) § Direction found by using rhr 2 on wire 1 § At location of wire 2 -> curled fingers point out of screen § Magnetic field pointing out of screen -> exerts a magnetic force on wire 2 which has a current of i2 -> in pic-> we know how to calculate the magnitude of this force. Since current in wire 2 and F field from wire 1 are perpendicular -> sinø = 1 § Susbtitue and solve for force / unit length that wire 1 exerts on wire 2 -> in pic § Apply rhr for magnetic force of 1 on 2 -> we see that wire 2 is attracted to wire 1 -> in pic owire 1 will also be attracted to wire 2 with a force of the same magnitude (opposite direction) -> in pic o If current in one of the wires is reversed -> repeat steps to show that wires repel each other o Magnetic force bw two parallel wires serves as the fundamental definition of the ampere § Ampere -> constant current in 2 straight parallel infinitely long conductors that produces an attractive force of 2E-7 N/m bw the wires when they are placed one meter apart in vacuum o In pic · Currents going in same direction -> attract each other! · Current in opposite directions -> repel each other!
· When a battery is hooked up to electrical devices the current in the circuit depends on? o Nearly all devices and wires have some? §Amount of this resistance, measured in? and represented with Greek capital letter?, depends on? o Consider device (chunk of material) attached to battery? § 1 ohm = 1V / 1A § In pic § When resistance is constant for any value of the applied voltage, this relation is also referred to as? · But the relation is always valid even if the resistance is a function of applied voltage · In pic o Resistance of material is related to? § Proportionality constant? § Analogy to understand the resistance of chunk of material? o Important equations and variables defined in pic
· When a batter is hooked up to electrical devices the current in the circuit depends on the particular device o Nearly all devices and wires have some resistance to the charge that flows through them §Amount of this resistance, measured in ohms and represented with Greek capital letter omega, depends on the material and the geometry of the device/wire -> in pic o Consider device (chunk of material) attached to battery -> if we divide the difference in voltage measured at each end of the chunk of material (voltage across the material), by the amount of current through the material -> result is resistance of the device / chunk of material § 1 ohm = 1V / 1A § In pic § When resistance is constant for any value of the applied voltage, this relation is also referred to as ohm's law -> in pic · But the relation is always valid even if the resistance is a function of applied voltage · In pic o Resistance of material is proportional to length of material and is inversely propoertional to the cross sectional area of the material through which the charge flows § Proportionality constant -> Greek letter row -> called the resistivity of material (ex in pic) § Analogy to understand resistance of chunk of material -> walk one end of head to the other · Number of people in hallway -> measure of resistivity of hallway -> easier to get from one end to the other (lower resistance) if hall is short and wide and has few people -> harder to get to other end (higher resistance) if hall is long narrow and crowded with people o Important equations and variabels defined in pic
· When a circuit contains a resistor and a capacitor -> current in the circuit changes? o In this circuit, when the switch is up (closed) -> the complete circuit consists only of? o When the switch is down -> battery is? § In this configuration -> the capacitor? o Apply kirchoffs loop rule to these? § Start at point A -> increase in voltage as we cross battery from - to + terminal of battery and a voltage drop ax the resistor · For the capacitor -> we can write the voltage ax the capacitor in terms of? o As we cross capacitor -> go from + to - plate which is a voltage? ·Since there are no more circuit elements this must add to? o Solving this expression for current in the circuit we see that §As the q on the capacitor increases, the current in the circuit? §Using calculus -> can be shown that for the charging capacitor circuit, the q stored on the capacitor and the current through the circuit are described by?
· When a circuit contains a resistor and a capacitor -> current in the circuit changes with time! o In this circuit, when the switch is up (closed) -> the complete circuit consists only of the outside loop and the battery charges the capacitor -> in pic o When the switch is down -> battery is removed and circuit consists only of the right hand loop -> in pic § In this configuration -> the capacitor discharges causing a current through the resistor for a short period of time o Apply kirchoffs loop rule to these circuits too § Start at point A -> increase in voltage as we cross battery from - to + terminal of battery and a voltage drop ax the resistor · For the capacitor -> we can write the voltage ax the capacitor in terms of the stored charge and capacitance -> when capacitor charges we see that + charge accumulates on top plate, so - charge accumulates on bottom plate o As we cross capacitor -> go from + to - plate which is a voltage drop (think E and what not) · Since there are no more circuit elements this must add to 0 -> in pic! o Solving this expression for current in the circuit we see that § As the q on the capacitor increases, the current in the circuit decreases until eventually the current = 0 when a maximum amount of charge is stored on the capacitor -> in pic § Using calculus -> can be shown that for the charging capacitor circuit, the q stored on the capacitor and the current through the circuit are described by exponential functions of time -> in pic
· When loop of conducting material (or portion of loop) moves with respect to a magnetic field? o flow? · Ex: loop of copper near end of bar magnet (B field at loop is not uniform here) o If loop and magnet are stationary? o As loop moves toward magnet? § When the loop moves? o Motion of loop -> creates a? o If loop is moved away from the magnet? · Another ex in which motion of part of a conducting loop can induce a motional emf o B field is uniform and bar is free to slide along parallel conducting rails o As bar slides at velocity (v)? §Resulting motional emf in the loop? o if v of bar is reversed?
· When loop of conducting material (or portion of loop) moves with respect to a magnetic field -> resulting B force on the charges in the conductor can create a motional emf in the conduction loop -> induced current in generated in the loop o Loop of conducting material has velocity -> thus charges in the loop have a v too -> charges experience a B force -> motional emf is created -> induced current is generated in the loop · Ex: loop of copper near end of bar magnet (B field at loop is not uniform here) o If loop and magnet are stationary -> no current in the loop o As loop moves toward magnet -> current is established in loop § When the loop moves -> charges in the loop gain a velocity in direction of the motion -> apply RHR and see that (for ex) + charges at the top of the loop experience a B force into the screen and the + charges at bottom loop experience a B force out of screen (similar for charges at any location for loop) o Motion of loop -> creates a motional emf in the loop -> induces current in the loop o If loop is moved away from the magnet -> B force on the charges in loop is reversed and induced current is in opposite direction · Another ex in which motion of part of a conducting loop can induce a motional emf o B field is uniform and bar is free to slide along parallel conducting rails o As bar slides at velocity (v) -> each charge in the bar is given that same v -> according to RHR-1, + charges feel a B force along the length of the bar (- charged electrons feel force in opposite direction) § Resulting motional emf in the loop -> induces a current as shown o if v of bar is reversed -> direction of the B forces, motional emf and induced current are also reversed
· When switch of RC circuit is in down position, we have the same kirchoff loop eqs as bf but with the? o Current turns out to be - in this discharging case which indicates that the? o The current initially starts out large when the charge stored on the capacitor at its? § Current drops to? § Calculus can be used to show that? §In pic § In pic -> important!
· When switch of RC circuit is in down position, we have the same kirchoff loop eqs as bf but with the emf removed o Current turns out to be - in this discharging case which indicates that the current through the loop when the capacitor discharges is in the opposite direction of the current in the charging case -> in pic o The current initially starts out large when the charge stored on the capacitor at its max § Current drops to 0 when there is no more charge stored on the capacitor § Calculus can be used to show that the stored charge and current in the discharging circuit behave as exponential functions of time. § In pic § In pic -> important!
· When we studied capacitors -> saw the the Ue (electric potential energy) stored in the capacitor depends on? o Think of this energy as being? o E field energy density (Energy per unit volume) -> is? · Similarly, when we studied inductors -> saw that? o Think of this energy as being? o Magnetic field energy is proportional to? · Energy density of an EM wave is = to? o Because amplitudes of E and B fields are related by speed of light -> we see that the B and E field energy density amplitudes are? § Simplify expression for total energy density o Because average of cos squared is = to one half - can write this expression for the average energy density of EM wave. Because of relation among E field magntidue, B field magnitude, and the speed of light -> can write expression? · Intensity of an EM wave -> average rate at which? o Represent intensity by Saverage -> can? E fields and B fields both have the potential to do work and thus can be viewed as a form of?
· When we studied capacitors -> saw the the Ue (electric potential energy) stored in the capacitor depends on the stored charge and capacitance (other equations for this too!) o Think of this energy as being stored in the E field bw the plates of the capacitor o E field energy density (Energy per unit volume) -> is proportional to the square of the E field magnitude -> this is a general result, true for any E field, not just the plates bw a capacitor · Similarly, when we studied inductors -> saw that the magnetic energy stored by the inductor depends on the inductance anc current through inductor o Think of this energy as being stored inside the magnetic field inside the inductor o Magnetic field energy is proportional to the square of the B field magnitude ->general result valid for any magnetic field · Energy density of an EM wave is = to the sum of the E and B field energy densities even when the E and B fields oscillate with time o Because amplitudes of E and B fields are related by speed of light -> we see that the B and E field energy density amplitudes are actually = (equivalent) § Simplify expression for total energy density o Because average of cos squared is = to one half - can write this expression for the average energy density of EM wave. Because of relation among E field magntidue, B field magnitude, and the speed of light -> can write expression several = ways · Intensity of an EM wave -> average rate at which the EM wave delivers energy to a surface area (Intensity = power / area) o Represent intensity by Saverage -> cane write in several = forms E fields and B fields both have the potential to do work and thus can be viewed as a form of energy storage (energy...?) kind of ??
Question · Assuming all of the resistors have the same resistance, which of the following correctly orders the equivalent resistance of the circuits shown? -> in pic
· b < d < a < c o remember reciprocal relationship for parallel! And solve! · Circuits (a) and (c) contain resistors connected in series. The equivalent resistance of a series combination of resistors is the sum of the individual resistances. Defining the resistance of each resistor as 𝑅R , the equivalent resistance 𝑅equiv, aRequiv, a for circuit (a) is · 𝑅equiv, a=𝑅1+𝑅2=2𝑅Requiv, a=R1+R2=2R · The equivalent resistance 𝑅equiv, cRequiv, c for circuit (c) is · 𝑅equiv, c=𝑅1+𝑅2+𝑅3=3𝑅Requiv, c=R1+R2+R3=3R · Circuits (b) and (d) contain resistors connected in parallel. The inverse equivalent resistance of a parallel combination of resistors is the sum of the inverse resistances. The inverse of the equivalent resistance 𝑅equiv, bRequiv, b for circuit (b) is · 1𝑅equiv, b=1𝑅1+1𝑅2=2𝑅1Requiv, b=1R1+1R2=2R · Thus, 𝑅equiv, bRequiv, b is half the resistance of a single resistor. · 𝑅equiv, b=𝑅2Requiv, b=R2 · The inverse of the equivalent resistance 𝑅equiv, dRequiv, d for circuit (d) is · 1𝑅equiv, d=1𝑅1+1𝑅2+1𝑅3=3𝑅1Requiv, d=1R1+1R2+1R3=3R · Thus, 𝑅equiv, dRequiv, d is one‑third the resistance of a single resistor. · 𝑅equiv, d=𝑅3Requiv, d=R3 · Therefore, the ordering of the equivalent resistances of the circuits is d < b < a < cd < b < a < c .
·Example question and set up in pic o Time for electrons to travel down wire depends on? o Rearrange current expression to solve for? o Each copper atom contributes? § And copper atoms -> 8.49E28 atoms / m^3 § In pic -> solving § Results in very small Vd for the electrons -> this is only? · Electrons themselves are actually moving much more? motion is? · Only the E field in the wire established by the battery causes the? ·In pic (electrons move opposite direction of E field as expected) § At this speed -> will take nearly? · How does bulb illuminate so quickly? · In pic answer
·Example question and set up in pic o Time for electrons to travel down wire depends on drift speed -> equation in pic o Rearrange current expression to solve for drift speed -> equation in pic o Each copper atom contributes 1 electron that is free to move throughout material § And copper atoms -> 8.49E28 atoms / m^3 § In pic -> solving § Results in very small Vd for the electrons -> this is only net speed of the electrons along the wire · Electrons themselves are actually moving much more quickly at speeds of 100,000 m/s or more -> but this motion is random! · Only the E field in the wire established by the battery causes the slow but steady drift of electrons down the wire at the calculated Vd (Vdrift) when switch is closed · In pic(electrons move opposite direction of E field as expected) § At this speed -> will take nearly 20 min for electrons to travel from switch to lightbulb · How does bulb illuminate so quickly -> wire and the bulb are full of electrons throughout their entire length -> all of these electrons drift down the length of the wire together at the same rate -> light bulb illuminates as soon as the electrons inside it start to drift in a uniform direction (don't have to wait 20 min for flashlight to turn on!) · In pic answer
∆Q? Vd? time (t) SI unit?
∆Q -> amount of charge that flows through an area (in a given amount of time) i = ∆Q / ∆t -can be used to find number of ions using the 1.602E-19 Vd (drift velocity) -> overall speed of electrons drifting through an area... (electrons themselves are actually bouncing around at very fast rate!) t (time) -> SI Unit is seconds
· An electromagnetic wave is traveling through free space. The amplitudes of the wave's electric and magnetic fields are 𝐸0E0 and 𝐵0B0 , respectively. The wave then passes through a filter that reduces the amplitude of the electric field by half (𝐸0/2)(E0/2) . What is the amplitude of the magnetic field after the wave passes through the filter?
𝐵=𝐵0/2 -> they have the same amplitudes always?? -> NO ?? (that's why the representation of EM waves can show just one tranverse wave??) +explanation next slide pic! +use equation in next pic! +amplitude of E field is much bigger than amplitude of B field according to the equation on the next slide!
