Electricity and Magnetism (Chap 5 & 11)
What is the force between two current carrying wires (one in magnetic field, other outside)?
if currents in parallel direction the wires will be attracted to each other. If opposite direction of current then wires will be pushed away.
RH rule to find direction when using F=qvB
v=fingers, palm=B, F=thumb (slap rule) ---this is for a positive charge. For a (-) charge the direction needs to be reversed
When does motional emf occur?
when a conductor moves in a magnetic field
electronvolt
work done when a charge equal to one electron charge is taken across a potential difference of one volt.
**AC Q
worked example 11.5
Symbol for into and out of the page
x = into the page dot= out of the page *Note: if arrow points upwards on the plane of the page it indicates an upward direction
Kirchhoff's current law (1st law)
ΣI (in) =ΣI (out) -- current coming into junction = current leaving the junction
Kirchhoff 's loop law (Kirchhoff 's second law)
ΣV=0 (around a loop)
magnetic flux
Φ=BAcosθ, A=area in the magnetic field, B normal to the loop area, units Weber
magnetic flux linkage
Φ=NBAcosθ
eqn. for Φ (magnetic flux) for an ac generator
Φ=NBAcosθ Φ = NBAcos(ωt) Φ= NBAcos(2πft)
emf eqns.
ε =W/q=P/I
potential difference
- The potential difference between two points is the work done per unit charge to move a point charge from one point to the other (work independent of path). - When there's a potential diff. there must be an electric field.
Magnet moved into and out of a coil of wire
- The current is created as a result of the motion of the magnet relative to the coil. - Current registered by the galvanometer increases when: • the relative speed of the magnet and the coil increases • the strength of the magnet increases• the number of turns increases • the area of the loop increases • the magnet moves at right angles to the plane of the loop.
capacitor
- Any arrangement of two conductors separated from each other by insulating material (or a vacuum) - stores electric energy
Forces acting on a current carrying wire in a magnetic field
- Consider an e- (see diagram). It's pushed down by the magnetic force. As e- move down there's a build up of negative charge at the bottom and positive at the top. The electric force from the e- prevent more e- from moving down. So qEv=qvB. Since they're balanced neither is responsible for a force on the wire. - The electric field E between the top and bottom sides of the wire exerts an electric force on the fixed positive charges inside the wire (the protons in the nuclei). It is this force that acts on the wire. F = (nAL)qE But qE = qvB, so: F = (nAL)qvB, F = (nAqv)BL Using nAqv = I, we get: F=BIL
Sources of power loss in transformers
- Eddy currents are tiny currents created in the core because the free electrons of the core move in the presence of a magnetic field. These currents heat up the core, dissipating energy. Laminated core eliminates eddy currents. - Magnetic hysteresis: the magnetic energy stored in the magnetic eld as the magnitude of the eld increases is not all given back as the eld magnitude decreases, resulting in power lost.
Why is the voltage high in transmission lines?
- P(loss)=RI² R=total resistance of cables - To minimise this loss it is necessary to minimise the current - P=VI, so if I is small V must be big
When happens when a rod moves through a magnetic field with constant speed (motional emf)?
- See pic. Rod is conducting (has free e-). magnetic field exerts a downward force on e- so there's a net negative charge at the bottom. The flow of e- to the bottom will stop eventually due to electrostatic repulsion. - An electric field is established in the rod: E = ε/L, ε=induced emf eE=evB (electric force e- back = magnetic force on e-) ε = BvL -Note: no current exists in rod except for a very short time period
diode bridge rectifier
- achieves full-wave rectification - During the first half cycle the current moves clockwise and enters the bridge through diode A. It then moves through the load from top to bottom and exits through diode C. During this half cycle diodes B and D do not conduct any current. In the next half cycle, the current is counter-clockwise. It enters the bridge through diode B and moves through the load from top to bottom again, i.e. in the same direction as the first half cycle. The current exits the bridge through diode D. *Note: to find direction of current know that the current will flow towards the (-) end.
Diode
- allows current to pass through it in only one direction and only when the potential at A is higher than that at B - a single diode results in half-wave rectification (disadvantage: 1/2 the power is lost)
Why do dielectrics increase capacitance (no voltmeter)?
- capacitor is connected to a battery that establishes a constant potential difference between the plate -Work is constant (W = qV ). The electric field in both is constant (W = qEd). This can only happen if the red electric field in Figure 11.32a is larger than that in 11.32b. -Implies that the charge q on the plates has increased due to the presence of the dielectric. So capacitance increases(C = Vq).
EMF vs. PD
- emf is the pd of a cell when no current is flowing through it - PD takes internal resistance into account
Rod slides on two wires that are joined by a resistor
- rod behaves like a battery (There is a potential difference between the top and the bottom equal to BvL) - work done to move e- to the bottom is W=FL= evBL - current equal to I=BvL/R is established in the resistor (because electrons in the bottom part of the circuit can move up through the resistor, thus momentarily reducing the number of electrons in the bottom. The electric field in the rod is reduced and so the downward magnetic force on the electrons pushes more electrons down) -rod needs to be pushed if it is to continue to move at constant speed. This is because the rod carries current I and is in a magnetic field, so it experiences a magnetic force F directed to the left given by: F=BIL=B(BvL/R)L =B²vL²/R - For speed to remain constant a force of equal magnitude needs to act on the rod. P generated by this force is: P=Fv=B²vL²/R - The power dissipated in the circuit as heat in the resistor is: P= ε²/R =B²vL²/R
How does a dielectric affect capacitance?
- ε > ε₀. Since C = εA/d , the capacitance with a dielectric is greater than that in a vacuum. why? - the capacitor (no dielectric) doesn't discharge because the infinite resistance of the voltmeter keeps charge from flowing - electric field between plates acts on the electrons of the dielectric, pulling them somewhat against the field. So there is separation of charge in the dielectric, known as charge polarisation. This creates a small electric field within the dielectric that is directed upward so the net electric field between the parallel plates is reduced compared to that in a vacuum. -work done to move charge q from one plate to the other is given:W = Fd = qEd . Since E is reduced, so is the work done.W=qV so potential difference across the plates has been reduced. From C = q/V , it follows that the capacitance increases.
What is the magnitude of electric field in a conducting sphere?
0, all the charge is evenly distributed on the surface
Steps to solve Kirchhoff 's law Qs
1 For each loop in the circuit, give a name to each current in each resistor in the loop and show its direction. 2 Indicate the direction in which the loop will be travelled. 3 Calculate ΣV for every cell or battery and every resistor: • For a cell or battery V is counted positive if the cell or battery is travelled from the negative to the positive terminal; negative otherwise. • For resistors the value of V is negative (−RI) if the resistor is travelled in the direction of the current; positive otherwise. 4 SetΣV=0. 5 Repeat for other loops. 6 Use Kirchhoff 's current law to reduce the number of currents that need to be found.
Order of magnitude of e- speed
10^15
AC generator
A coil is made to rotate in a region of magnetic field. Can be done by: a diesel engine burning oil, by falling water in a hydroelectric power station, by wind power, etc. The ends of the coil are firmly attached to two slip rings that rotate along with the coil. The slip rings touch carbon brushes that transfer the current into an external circuit.
Insulator
A material without free e-
RH rule to find direction when using F=BILsinθ
F= thumb, I= fingers, B= palm — θ is between I and B. For a (-) charge the direction needs to be reversed
resistors
Conductors whose resistance cannot be neglected are called resistors
AC vs DC current
DC: is when all electrons move in the same direction. AC: electrons do not drift in the same direction but oscillate back and forth with the same frequency as that of the voltage. The flux and the emf are out of phase by 2π or 90°.
Ohmic materials
Follows Ohm's law
What's another eqn. for E?
E=kQ /r²
How does changing the temp affect resistance?
For most metallic conductors, increasing the temperature increases the resistance.With an increased temperature the atoms of the conductor vibrate more and this increases the number of collisions per second.This in turn means that the average distance travelled by the electrons between collisions is reduced, i.e. the drift speed is reduced.This means the current is reduced and so resistance increases.
A loop of wire has its plane horizontal and a bar magnet is dropped from above so that it falls through the loop with the north pole first Find the direction of the current induced in the loop.
If induced emf increases current's direction needs to be switched. If emf decreases current's direction is the same.
Relation between work done by/on charges and potential diff.
If we move the charge q between two points whose potential difference is V, we will have to do work qV.We are assuming that the charge is moved slowly and with constant speed from one point to the other. If, on the other hand, the charge is left alone in the electric eld, the electric forces will do work qV on the charge; this work will go into changing the kinetic energy of the charge. Ek may increase or decrease
Why use potential divider over conventional arrangement?
In the conventional arrangement (see pic) the voltage can be varied from zero volts up to some maximum value less than the emf. With potential divider, voltage can be varied from 0 to emf.
Ohm's law
I∝V
Lenz's law
Lenz's law states that the induced emf will be in such a direction as to oppose the change in the magnetic flux that created the current. It is equivalent to energy conservation.
Do transformers change the frequency of the voltage?
No
Does the magnetic field do work?
No, because field is perpendicular to the direction of v.
V-I graph for a thermistor
Notice axes are switched
Power dissipated by a resistor eqn.
P = IV
Ampere
The ampere is de ned through the magnetic force between two parallel wires. If the force on a 1 m length of two wires that are 1 m apart and carrying equal currents is 2 × 10−7 N, then the current in each wire is de ned to be 1A
drift speed
The average speed with which the electrons move in the direction opposite to the electric field
Faraday's Law
The induced emf is equal to the (negative) rate of change of magnetic flux linkage, that is: ε=−N∆Φ/∆t (negative sign not important)
What is needed to make charges move?
To make charges move in the same direction we need an electric eld to exert forces on the charges. To have an electric eld means there must be a potential difference. So something must provide that potential difference. Cells use the energy from chemical reactions to provide potential difference.
Faraday's Law Q
Using ε=∆Φ/∆t and Φ=BA, ε=B∆A /∆t ε=BLv∆t/∆t ε=BLv
Graph of V vs t for ac generator as the armateur rotates
V (emf)= slope of Φ vs. t graph
Deriving I=nAvq
V=AvΔt q= AvnqΔt n=no. of e-, q=charge of e- I=∆q∆t I = nAvqΔt/Δt I=nAvq
Voltage, current and power eqns. for AC in terms of ω
V=V₀sin(ωt)= ωNBAsin(ωt) I=I₀sin(ωt)= ωNBAsin(ωt)/R P =V₀I₀sin²(ωt)= (ωNBA)²sin²(ωt)
eqn. for emf
V=−dΦ/dt V = ωNBAsin(ωt)
How can a galvanometer be converted to a ammeter or voltmeter?
Voltmeters and ammeters are both based on a current sensor called a galvanometer.An ammeter has a small resistance connected in parallel to the galvanometer and a voltmeter is a galvanometer connected to a large resistance in series.
Peak voltage produced by an ac generator
V₀ = ωNBA
Eqns. for electrical work
W = FL = qEL=qV= V/d
Eqns for energy stored in a capacitor/ work done to move charge from one plate to another
W = q²/2C= qV/2= CV²/2 (last one in data booklet) E=q²/2C =qV/2=CV²/2
Converting from eV to J
W(J)= W(eV) x e
When is there no magnetic force on a charged particle?
When the particle is not moving or if it moves along the field lines. F=qvBsinθ (where v and B must be perpendicular, θ is between v and B)
Primary cell
a cell that can only be used once (until it runs out) and is then discarded
secondary cell
a cell that is rechargeable and can be used again.
Voltmeter
a device that can be connected in parallel to measure potential diff. Ideal voltmeter= infinite resistance
Ammeter
a device that can be connected in series to measure current. Ideal ammeter= 0 resistance
transformer
a device that takes a certain ac voltage as input and delivers a different ac voltage as output. It consists of two coils wrapped around a common iron core. The primary coil is the one connected to the input ac source. Since flux of primary coil is changing an emf is induced in the secondary coil.
Magnetic flux density
another name for magnetic field strength B
why do wires heat up?
as e- flow through conductors they undergo inelastic collisions. They lose energy to the atoms. These atoms gain Ek and start vibrating faster so there's an increase in temp.
Capacitance
charge per unit voltage that can be stored on the capacitor. (can just eqn)
emf
emf ε (of a battery) is the work done per unit charge in moving charge from one terminal of the battery to the other.
What does resistivity depend on?
material of the conductor, temp
Conductor
materials that love free e-. The free e- act as charge carriers when a potential difference acts across a conductor. Current exists when charge carriers move.
What creates magnetic fields?
moving charges
When do charges move inside a conductor?
only if there's a potential difference established in the conductor
Which direction does current flow in?
positive to negative
If the velocity of a charge is perpendicular to the magnetic field it is in, what motion does the charge undergo? Describe it using equations (find T).
qvB=mv²/R R=mv/qB T = 2πR/v T = 2πmv/vqB T = 2πm/qB --- T is independent of v
capacity
the amount of charge a cell can deliver to an external circuit in its lifetime
electric field strength
the electric force per unit charge experienced by a small, positive point charge q (vector-direction same as that of the force experienced by a positive charge ).
internal resistance
the resistance of the contents of a cell/battery. This resistance causes some of the power delivered by the cell to drive the current through the circuit to be dissipated.
Resistors in series
there is no junction in the wire connecting the two resistors so the current flowing through both is the same
why does a transformer have an iron core?
to ensure that as much of the flux produced in the primary coil as possible enters the secondary coil. Iron has the property that it confines magnetic flux and so magnetic eld lines do not spread out into the region outside the core.