Physics 104 Exam 1

Adding forces -In which case is the net force on q bigger? -> in pic +explain? -draw what?

-Case 1 --> in pic +look at each force/part and then find the total (net force) +answer is true if q is + or - (pic shows case 1 as if q is +) +Case 1 --> Fnet is > 0 (forces add together) +Case 2 -> Fnet = 0 (forces acting on q cancel out) -draw all forces acting on objects (basically a free body diagram!!)

Lecture 2 - Electric forces -main topics for day?

-Coulomb's Law -Adding forces with multiple charges -Electric dipoles -Induced dipoles -Labs meet this week!

question; in pic

-answer --> b +2q has larger magnitude and thus will push/repel the charge overall more the right. -q will still pull/attract the charge down.

Adding forces as vectors, again -The net force on q 3 is the sum of two force vectors. This sum is best represented as: --> in pic +explain? +Fnet here?

-in pic -> A +likes repel and opposites attract with straight line bw the charges +Y components cancel and only X component is left (connect tail to tip to get Fnet vector --> in pic)

Shocking truth about electric animals video (bridge set) Transcript highlighted below (in doc)

Shocking truth about electric animals video (bridge set) Transcript highlighted below Hank Green: What you're about to see in this SciShow Dose may shock you. There are about 8600 animals in the world that are electroreceptive. They can feel electric fields. Like the sense of touch, eletroreceptivity carries information about the shape, size, and texture of things in the environment, and like hearing or vision, it works at a distance, but what it actually feels like is something that we will never be able to even imagine. For electroreceptive animals, electric currents and electric fields are as real and immediate as color or music are for us. Most electroreceptive animals are amphibians or fish, though there are rare exceptions, including the duck-billed platypus, because everything that could possibly be weird about the platypus is weird. Electroreceptivity has evolved over and over again, totally independently, in a global act of convergent evolution. Animals that live and hunt in murky water where they might not be able to see or hear very well gain advantage if they can feel their surroundings through special electroreceptive cells in their skin. And a few animals take it even further. There are 716 known species of fish capable of electrogenesis, the creation of electric fields and even strong electric shocks. And these fish don't have a common ancestor either. Biologists believe that electrogenesis has evolved separately at least 11 different times in places as isolated from each other as the African interior, the Amazon basin, and the coral-rich waters of Australia. The most famous electric fish is the electric eel, which is electric but is not an eel--it's actually a kind of knifefish that lives in South America and can produce an electric shock up to 600 volts--enough to hurt, but not seriously injure, something as big as a human, but if you're an itty bitty tiny fish trying to go about your daily business of swimming and eating and not dying, yeah, 600 volts is the last problem you'll ever have. All cells in living things produce an electric charge; it's a normal part of cell biology. They do this by pumping positive ions of metals like sodium, potassium, and calcium outside the cell membrane. So the outside of your cells are slightly positive compared to the insides. Every cell in your body has a resting voltage of about 0.085 volts. Of course, my cells aren't organized in a way that would let me add those voltages together, but this fish have special cells called electrocytes, they're stacked in long chains like the batteries inside a flashlight. And each one of those cells is connected on one side to a nerve fiber. When an electric eel charges up, its brain sends a signal down those nerve fibers. When the signal hits the electrocytes, little pores open up in their cell membranes, allowing those positive ions to rush into the cell. Each cell becomes like a little tiny battery. Instead of having a negative inside and a positive outside, the cell now has a negative left side and a positive right side. And just like in a battery, electrons flow between the two ends to equalize the charge. Since the cells are stacked in chains, positive to negative to positive and so on, the voltage of each cell adds up with every other cell in the chain. String enough of those chains together and fire them all at once, and bleaughh, underwater barbecue. But this arrangement of electrocytes doesn't have to be used offensively, and in most electric fish, it isn't. Instead, they create a constant electric field around themselves, usually with the power of only a few millivolts. They use this to sense their immediate environments so they know when food or predators are nearby, even in total darkness. And some species of fish use these electric fields to like, communicate with each other. Using distinct patterns of discharges, they can signal aggression, submission, alarm, even courtship. When they're ready to mate, the males and females of many kinds of electric fish will perform electric duets. Electric boogie! So if you feel like you're missing out, you might be wondering, why didn't we evolve to create awesome electric fields that we can control with our minds? Well, because we can see and hear. Seeing and hearing may seem kind of boring compared to being like, electric fish Magneto, but they use a lot less energy than electrogenesis. Plus, one of the most common questions people ask about electric eels is 'why don't they electrocute themselves?' The answer being that they do. When an electric eel fires, you can actually see it flinch. I don't know about you, but I think I'll stick with my senses since they don't actually cause physical pain to use. Thanks for watching this electrifying SciShow Dose, and if you'd like to help us keep sharing natural wonders like this, go to Subbable.com/SciShow to find out how you can help us keep our batteries charged, and don't forget to go to YouTube.com/SciShow and subscribe. [Endscreen] English

There are several ways of creating a what? -Friction? +ex? +ex? -But why does charge flow in this way? When you rub fur on a rubber rug, why does the fur gain a positive charge and the rubber gain a negative charge? Why is it the reverse when you rub silk on a glass rod? +ex and ideas? +precipitation (p) static? -conduction? +ex? +ex? -Induction? +ex with neutral conductor and positive insulator? +ex with neutral insulator and positive insulator?

There are several ways of creating a net charge on solid objects, some of which you are already familiar with. -Friction-- rubbing two objects together can dislodge electrons from one. Those electrons can then be taken up by the other, creating net charge on both. +If you've ever walked across a thick carpet, you have already very likely experienced the transfer of charge through friction. +Likewise, if you ever dove into a box full of packing peanuts-- You should have noticed how the peanuts stick to your fur. That's because electrons in your fur are rubbed off onto the peanuts, which gain a negative charge, leaving your fur with a positive charge. Instant attraction. -The answer is in something called the triboelectric series. Tribo is from the Greek for "rub." The chart to the right shows which materials are likely to gain a positive or negative charge if you rub them together. Notice that the same material won't always gain a positive or negative charge. +If you rub your hands against polyester, your hands will likely gain a net positive charge, and the polyester will gain a net negative charge. Suppose you now rub a PVC pipe against polyester. In this case, the pipe will likely gain a net negative charge, and the polyester will gain a net positive charge. +One important case of the movement of charge through friction is called p static or precipitation static. As an airplane flies through heavy clouds, friction between the plane's fuselage and the clouds transfers electrons to the plane. The charge that builds up on the plane can interfere with communications and cause a variety of other problems. -conduction --> Charge can be transferred through direct contact between two objects if one already has a net charge or through a spark if the charged buildup is large enough. +After dragging your feet along that carpet, you've probably experienced conduction when you reach out to a doorknob. You often get zapped by a little shock just by touching it. +During your stroll, you picked up electrons from the carpet fibers through friction. Because those electrons are repelling each other, they are ready to rush from your hand the moment you touch the metal doorknob. Often you've built up enough charge so that the electrons don't wait for contact. They leap off your fingers, creating a tiny spark that you can sometimes see. -induction --> The charge in an object might not be changed, but simply rearranged so that the different parts of a single object show different kinds of net charge (object becomes polarized basically...) +Suppose we have two objects. One, a, is an insulator with a net positive charge, and the other, b, is a conductor that is electrically neutral, so no net charge. --> If we bring these two objects close together but don't let them touch or get near enough for a spark to pass between them, what will happen? No charge will move from one object to the other, but their proximity will cause charge to redistribute itself in the conductor in which electrons can move freely. --> The proximity of the positive charge will cause electrons to move toward the side of b, which faces a. Meanwhile, the side of b furthest away from_a will have a positive charge, the positively charged atoms that the moving electrons left behind. The net charge on b remains zero. By bringing it close to a, we just rearrange the distribution of charge in it (in pic) +What happens if object b is an insulator? In the first approximation, we can say that since charges can't move around freely in an insulator, there is no motion of charge in object b. However, this isn't completely accurate. Charges in insulators have trouble moving between atoms that make up the material and so can't travel much distance. But bringing an external charge close can induce a separation of charges within the insulator's atoms. In other words, we can create small dipoles within the insulator (in pic) just think of dipoles as objects with separated positive and negative charges from end to end. V. This effect is why you can stick a charged balloon to a wall even if the wall isn't made of a conducting material.

Prelecture 3b Video about physics behind touchscreens?

Transcript (highlighted in word folder) Watch the video about how touchscreens make use of capacitance when you touch them (transcript highlighted below) https://youtu.be/wKuqNuzM1oM Touchscreens are everywhere. Not just in smartphones, but in supermarkets, ATMs, and even airplane seats. And you may have noticed that not all touchscreens are the same. The old-school touchscreens can be pretty tough to use -- sometimes it feels more like a push-really-hard-screen instead of a touchscreen. On the other hand, certain smartphones and computer monitors are really responsive to many different touch patterns. There are lots of different technologies out there, but they're all trying to achieve the same goal: sending precise electrical signals from specific locations on the screen. One of the most widely used types is the resistive touchscreen, where you have to physically push and bend the screen to make it work. Resistive touchscreens are made of two separate layers: The top layer is made from a flexible and transparent material, such as polyethylene, which is a common plastic used to make things like soda bottles. And the bottom layer is made of something more rigid, like a sheet of glass. To make the screen work, both of these layers are thinly coated with some sort of metal compound that conducts electricity, like indium tin oxide -- which is commonly used because it's transparent. These layers are also separated by tiny insulating dots, which /don't/ conduct electricity, called spacers. They keep the screens apart to make sure there aren't any false touch signals. When the screen is on, a small voltage is applied across the screen in both the horizontal and vertical directions. As soon as you push down on the flexible screen with anything, like your finger or a stylus, it connects the two layers together. This changes the voltage, and a small processor connected to the screen can calculate exactly where you pressed in X and Y coordinates. These resistive touchscreens are pretty affordable and durable. So, they're useful for things like credit card readers in grocery stores, where you need to capture touch data of a messy signature -- over and over again. But they can be a little frustrating to use if you don't push hard enough. Plus, they normally can't understand multiple-touches at the same time - so they're no good for two-finger zoom or more complex tasks. That's why these days, most smartphones rely on capacitive touchscreens, where your finger becomes a key part of the electronics. There are different kinds of capacitive touchscreens, and they can vary from device to device. But one basic design is a sheet of glass containing a grid of hair-thin lines of a conductive metal, like indium tin oxide. The grid lines in one direction are called the driving lines, which provide a constant electric current. And the lines in the other direction are called the sensing lines, which detect this electric current. At every point where the sensing lines and the driving lines cross, there will be a specific electrostatic field, which is registered as neutral by the processor in your smartphone or computer. But that all changes when something conductive comes along and touches it -- like your finger. See, the human body has a natural capacitance, which means our bodies can conduct electric current, and can store electric charge. So when your finger touches the screen, the charge in the screen is drawn around that point, distorting that electrostatic field. The electricity doesn't actually /flow/ through your finger. Basically, the electrostatic field feels the effects of your electric charge and redistributes itself accordingly. Even really small changes are detected by the processor, which can then interpret the patterns you're making - whether it's a tap or a slide. Because the lines of the grid are so thin, capacitive touchscreens are super accurate, and some versions can process multiple touches at a time. But they won't work if you have gloves on -- because the cloth isn't conductive, unless your gloves have those special fingertips with metal fibers inside. Plus, something like sweat can affect how electricity is conducted across the screen, because it's full of salts. It's all about the materials that can affect the electrostatic field generated inside your screen. So next time you're texting on a smartphone or scrolling through internet forums on a tablet, just remember: you're actually a part of the electronics making it work. Thank you for watching this episode of SciShow, which was brought to you by our patrons on Patreon. If you want to help support our show, you can go to patreon.com/scishow. And don't forget to go to youtube.com/scishow and subscribe resistive touch screen -> touching of the two layers registers the touch (in pic) capacitive touch screen -> disturbance of electric field by finger touch (finger is slightly capacitive and stores some charge) --> sensing and driving lines!

pic last slide

in pic

Lecture 1; Today's agenda

in pic -outline for day

pics last slide

in pic (summary slide)

Question (in pic)

o 𝑉A=𝑉B they are both the same magnitude of charge and they are both the same distance from A. Thus, they cancel to 0 bc they have = electric potentials but opposite signs. Same reasoning with B + V=KQ/r

Question; Question: A charge is moving in a constant electric field along the path shown. (in pic) -When it reaches its final poistion, has electric potential energy been lost, gained, or has it stayed the same +Explain?

- Its been lost! (+ work is done) +Explain: electric field could be coming from the left from + source charge and thus moving towards the + would decrease PE (be favorable). Electric field could also be coming from the right as a - charge and thus moving away from the - charge would decrease PE (be favorable!)

-2 charged particles separated by some distance have some? +in pic -Capacitors -> structures that ? +capacitor can be used to? +If charged capacitor is hooked up to an electric circuit? +in pic -Topics to be covered?

-2 charged particles separated by some distance have some potential energy associated with them previous pre lecture +in pic -Capacitors -> structures that store equal amounts of + and - charge generally separated by a small distance -> +capacitor can be used to store electric potential energy +If charged capacitor is hooked up to an electric circuit its (capacitors) stored potential energy can produce a current in the circuit +in pic -Topics to be covered o Capacitance what is meant by it o Parallel plate capacitors understand how the capacitance of a parallel plate capacitor depends on its geometry o Electric potential energy stored in a capacitor calculate o Series and parallel combinations of capacitors explain and calculate the effects of combining capacitors in series and parallel arrangements o Dielectrics in capacitors describe how and why the capacitance of a capacitor increases when an insulation material other than air is placed bw the plates of a capacitor

Interactions between charges -A negatively-charged rod is brought near a neutral metal sphere, without touching. Which image best represents the distribution of actual charges within the sphere? (in pic) +explain?

-A --> in pic; - charges are free to move in conductors (+ charges can not move much!)... charges cant move much in insulators +a - charge causes the electrons to move away from it as shown in A --> also consider that this asks for total/actual charge and NOT net/excess charge! +It is A and NOT C bc + charge in conducting (and insulating) material cannot move (restriction from lattice structure) --> only electrons can move (in both conducting and insulating material, but - charges move much more freely in conductors and are pretty restricted in insulators) +could be C if it was a fluid with + and - charges that are free to move around possibly +C could also represent the net/excess charge (more or less) +D would be right if it was an insulator --> electrons cant move much in insulators (small dipoles form in "polarized state")

Grounding -A conductive connection to the Earth is known as a? +this allows? +a + vs a - object? - -However, grounding is not synonymous?

-A conductive connection to the Earth is known as a ground. (ground --> connect object to another object with lots of charge/electrons....) +A ground allows an object to "share" electrons with the Earth (essentially a very large supply of charge). +a + object --> electrons flow from the earth into the object +a - object --> electrons flow from the object into the earth -However, grounding is not synonymous with neutralizing. (i.e., a grounded object will not always automatically become electrically neutral.) Let's look at an example...

Electroscope -The electroscope has been given a net negative charge by the PVC pipe. What will happen when the positively charged acrylic rod is brought nearby without touching? +explain?

-A) The leaves will get closer together. +PVC pipe gives the electroscope a - charge and thus the leaves spread apart due to this excess - charge (electrons) --> + object attracts excess electrons in the leaves to the ball and makes the leaves become more neutral (less - because electrons leave the leaves) --> leaves repel less and move closer together (basically, + charge polarizes and brings some - charge away from the leaves)

-All matter contains? +We know this through? >Ex? >Ex? >Various combinations of the rods and the fur/silk show that? -Properties of matter +Electric charge can be? +Objects with equal amount of + and - charge are? +Mass can only be? -Charged objects exerts what on each other? +Same sign charges? +Opposite sign charges? -Charge is what? explain? -Atoms are made of what 3 particles? +explain all 3 -Charge can be? +Typically done how? >Ex? -Charge is what? it only comes in? (Amount of charge Ne) +Smallest chunk of free charge? -SI unit of charge?

-All matter contains + and - charge +We know this through observation >Ex: rub rubber rod and fur --> - rod and + fur (-->) rod and fur attract >Ex: rub glass rod and silk --> - silk and + rod rod and fur attract >Various combinations of the rods and the fur/silk show that opposite signs (+/-) attract and same signs (+/+ or -/-) repel -Properties of matter +Electric charge --> can be + or - +Objects with equal amount of + and - charge electrically neutral +Mass --> can only be + -Charged objects exerts forces on each other +Same sign charges (+/+ or -/-) --> repel +Opposite sign charges (+/-) --> attract -Charge is conserved --> only equal quantities of + and - electric charge can be created or destroyed by a physical process -Atoms --> made of 3 particles +Nucleus >Protons --> + charge >Neutrons --> neutral charge, 0 +Electrons --> - charge, attracted to and orbit around the + nucleus -Charge can be transferred between objects +Typically done by removing electrons from one objects and depositing them onto another object >Ex: rub rod and fur -Charge is quantized charge only comes in finite chunks (Amount of charge Ne); fundamental charge is N and is in units of e (e is -1.602E-19), 1N = 1e = 1.602E-19?? +ex: A certain lightning bolt moves 20.0 C of charge. How many units N of fundamental charge e is this? --> 20C / (1.602E-19) = 1.25E20.... think 1.602E-19 / 1e ?? +Smallest chunk of free charge --> magnitude of charge of a proton/electron --> 1.602E-19 C (coulombs) (charge of electron and proton are equal in magnitude but opposite in sign, proton is + and electron is -). -SI unit of charge [Charge] = Coulombs (C)

Electroscope -An electroscope allows us to? +When the metal "leaves" have a net electric charge? +what happens ex? -structure of electroscope? -neutral leaves? +leaves with charged object near or even touched ball?

-An electroscope allows us to detect the presence of electric charge (cant tell sign of charge tho)... senses presence of external charge (charge detector!) +When the metal "leaves" have a net electric charge, they separate. +ex: - charge brought near ball --> excess - charge (electrons) are repelled to the leaves and thus leaves have excess - charge and repel one another, and excess + charge gather on ball +ex: + charge brought near ball --> excess - charge (electrons) are attracted to the ball --> excess + charge and thus leaves have excess + charge and repel one another +electroscope is basically polarized by a charged object and then the leaves spread apart (bc leaves have same excess charges on them and repel)... (leaves dont move if object is not charged....) -conducting rod and ball (in pic) with thin metal leaves attached to the rod. leaves (and part of rod) are surrounded by enclosure to protect from outside (other forces and what not that could interfere!) -neutral leaves --> leaves hanging down (pic on left) +middle pic --> object is brought near (maybe touched?) --> charged rod polarizes the electroscope and leaves spread apart +right pic --> near stronger charged object (or touched with charge)

Transferring charge -A PVC pipe is rubbed with a silk cloth. Which of the following correctly summarizes the charge on each object and the force between them after being rubbed together? +explain? -triboelectric series +gaining vs losing electrons? -same vs oppostive charges? -need something with known charge to?

-B) Pipe is negative; silk is positive; they attract +look at triboelectric series to determine which object will gain electrons (negative charge) and which will lose electrons (positive charge) when the objects are rubbed together --> in pic -shows which direction charge will be exchanged when objects are rubbed together. That is, shows which object will gain electrons (- charge) and which object will lose electrons (+ charge) when objects are rubbed together --> in pic! (shows which object will give up and which will accept electrons basically when the objects are rubbed together) +gain electrons --> object becomes more - (electrons have - charge) +lose electrons --> object becomes more + (electrons have - charge) -same charges --> repel +opposite charges --> attract -need something with known charge to determine charge of unknown object

Charging by induction -A negatively-charged rod is brought near a conducting metal sphere without touching. The sphere is then grounded while the rod is still present. The ground is removed, and finally the rod is removed. What is the final charge on the sphere? +explain?

-B) Positive +in pic --> the - rod polarizes the sphere so excess + charge is close to the rod and excess - charge is far away from the rod --> excess - charge (electrons) are by the grounding connection and thus flow into the earth --> when grounding and then rod are removed, the object retains the + charge bc it lost electrons previously!

How many electrons? -Suppose the pipe acquires an overall electric charge of -2 x 10 -4 Coulombs (C). About how many individual electrons were transferred? +explain? -review what?

-C) 10 15 electrons +NOT A or B bc you cant exchange fractions of electrons (can only move/exchange whole number integer electrons) +use dimensional analysis (will come in handy a lot in this course!!) --> know that charge of single electron is -1.602E-19. -review --> scientific notation and "preunits" (femto, milli, pico, nano, etc...)

-Capacitance? +Nearly any pair of surfaces insulated from one another can be? -Membrane of every cell in your body? +Negative charges and + charge accumulation? +Bc membrane stores charge its a? +In pic -In electric circuits capacitors are generally made of? +Typically draw capacitor with? +In pic -Parallel-plate capacitor made of? +Positive charge ? +Identically amount of negative charge with a ? +In pic -Using Gauss's law? +In pic +Net electric field at any point in space due to all the charges of the capacitor is the? +In pic -Potential difference bw the plates given by the? +In pic +Magnitude of charge stored on one of the plates is proportional to? >This proportionality constant is called the? >Capacitance depends on (constant)? >Capacitance always depends only on the? >Units of capacitance? In pic In pic In pic -Summary in pic

-Capacitance measure of the ability of a structure (capacitor) to store charge +Nearly any pair of surfaces insulated from one another can be a capacitor -Membrane of every cell in your body electrically insulating phospholipid bilayer +Negative charges accumulate on interior layer of membrane -> attract + charges to the outer layer of the membrane +Bc membrane stores charge it's a capacitor +In pic -In electric circuits capacitors are generally made of 2 metallic surfaces (often called plates) +Typically draw capacitor with 2 parallel lines representing the plates and electrical connection to each plate +In pic +Parallel-plate capacitor made of 2 parallel surfaces separated by a very small distance (relative to the size of the plates) +Positive charge, with corresponding surface charge density (sigma) on top plate +Identically amount of negative charge with a corresponding surface charge density (Sigma) on the bottom plate +In pic -Using Gauss's law calculate electric field due to the sheets of charge +In pic +Net electric field at any point in space due to all the charges of the capacitor is the vector sum of these 2 electric fields +In pic -Potential difference bw the plates given by the electric field multiplied by the plate separation +In pic +Magnitude of charge stored on one of the plates is proportional to the potential difference bw the plates >This proportionality constant is called the capacitance of the capacitor. >Capacitance depends on Epson (naught) permittivity of free space, which describes the electric properities of the space bw the plates and the geometry of the capacitor >Capacitance always depends only on the geometry of the two plates and material bw them. Eo = 8.85E-12 ?? >Units of capacitance C/V = F (farads) In pic In pic In pic ·-Summary in pic

Summary slide -Capacitors devices that? +Capacitance of a structure depends only on? +In pic -Can write the energy stored in a capacitor in? +in pic -Several capacitors can be hooked together in? +in pic (didn't talk about in prelecture or readings!) +When capacitors are attached in series? +in pic +When capacitors are attached in parallel? +In pic -If dielectric material other than air is placed bw the plates of a capacitor the resulting capacitance is? +in pic Bridgeset video same as M1 video!

-Capacitors devices that store charge and electric potential energy +Capacitance of a structure depends only on its geometry and the material bw the plates (doesn't depend on charge or voltage don't be confused by eqs in pic!) +In pic -Can write the energy stored in a capacitor in 3 identical ways depending on which 2 of the 3 quantities (q, V, and C) we happen to know +In pic -Several capacitors can be hooked together in series of parallel (Didn't talk about in prelecture or readings!) +in pic (didn't talk about in prelecture or readings!) +When capacitors are attached in series they each store the same charge and their potential differences add +In pic +When capacitors are attached in parallel the potential difference ax each capacitor is the same and the total charge stored is the sum of charges stored by each capacitor +In pic -If dielectric material other than air is placed bw the plates of a capacitor the resulting capacitance is greater than the capacitance of the air filled capacitor +in pic -NOT COVERING CAPACITORS IN SERIES OR IN PARALLEL Bridgeset video same as M1 video!

-Compare electrical potential energy to? +Think what? -When gravitational potential force does + work on an object as it falls? +If object moves at some angle theta with respect to the downward direction, the change in gravitational potential energy depends only on? (in pic) -Electric force is also a? +Consider + charge q. When electric force does + work on this + charge? (in pic) -When electric field does - work on the + charge? (in pic) -Only the component of the charge's displacement where matter? (in pic) -If the charge is negative, when the charge is displaced in a direction opposite to the electric field then the electric field does? (in pic) -Negative work is done when the negative charge is? (in pic) -Basically think of?

-Compare electrical potential energy to gravitational potential energy (near surface of earth); +Think electric field could be coming from either + or - charge (positive would have arrows coming from it and - would have arrows coming towards it) think about if it would be favorable (decrease PE) or unfavorable (increase PE) for charge to move closer to or farther from either of the hypothetical +/- charges! -When gravitational potential force does + work on an object as it falls, the gravitational potential energy associated with the object decreases +If object moves at some angle theta with respect to the downward direction, the change in gravitational potential energy depends only on the component of motion parallel to the gravitational force (red in pic) conserved force (in pic) -Electric force is also a conservative force with an associated electric potential energy +Consider + charge q. When electric force (field....) does + work on this + charge, causing displacement in direction of the electric field, the electric potential energy associated with the charge decreases (in pic) -When electric field does - work on the + charge due to displacement in the opposite direction of the electric field, the electric potential energy associated with the charge increases (in pic) -Only the component of the charge's displacement parallel to the electric field matters (just like with gravitational potential energy) in red in pic -If the charge is negative, when the charge is displaced in a direction opposite to the electric field then the electric field does + work on the charge and the associated electric potential energy decreases (in pic) -Negative work is done when the negative charge is displaced in the same direction as the electric field, increasing the electric potential energy (in pic) -Basically think of where the charge wants to go, if it goes where it wants to go (- charge wants to go toward electric field and + charge wants to go away from electric field) then the electric potential energy decreases...askaboutcosignthetapart!!

-Completely uncharged capacitor? +in pic -Once plates have a single + and - charge it takes? +Every time another charge is stored on the plates it takes? +Negative charge is going from + to - here and thus? +In pic -Net result is that the total electric energy stored in a charged capacitor is equal to? +Capacitance of a capacitor relates the? +We can write the electric potential energy stored in a capacitor in 3 different? + In pic -What we know about the charge and voltage ax the capacitor helps use choose which? +Capacitance of a capacitor is always? +So when a capacitor is attached to a circuit sometimes we know info about the electric potential bw the plates? +Know about stored charge use expression? +Can use expression with q and V can be? · -Summary in pic

-Completely uncharged capacitor stores no electric energy it effectively takes no energy to move the first - charge from one plate to the other (after - charged moves, the plate it moved from becomes + and the plate it moves to becomes -)... both plates started as neutral and uncharged... +in pic -Once plates have a single + and - charge it takes work to add the next - charge +Every time another charge is stored on the plates it takes even more work to add the next charge. Negative charge is going from + to - here and thus is unfavorable and takes more work as more charge is added +In pic -Net result is that the total electric energy stored in a charged capacitor is equal to one half the value of that charge multiplied by the resulting potential difference bw the plates +Capacitance of a capacitor relates the stored charge and potential difference between the plates +We can write the electric potential energy stored in a capacitor in 3 different but = ways +In pic -What we know about the charge and voltage ax the capacitor helps use choose which eqs to calculate the energy stored by the capacitor +Capacitance of a capacitor is always constants! +So when a capacitor is attached to a circuit sometimes we know info about the electric potential bw the plates use expression with C and V +Know about stored charge use expression with C and q +Can use expression with q and V can be tricky if charge and voltage are changing (bc its easy to forget that if one of them changes the other must also change) often better to use the other 2 expressions, but this one can work at times ! -Summary in pic

Coulomb's law -Coulomb's law describes? +This is known as the? -equation? +constant, k? +F is what? +type of relationship with distance? +q's are what? -each charge does what? +opposite vs like charges? -2 charges exert what magnitude of force on other?

-Coulomb's law describes the force between two electric charges. +This is known as the electric force or the Coulomb force. -in pic +in pic +F is the magnitude of the charge +inverse square relation +absolute values of q are used -each charge exerts a charge on the other force +opposite charges attract and like charges repel -2 charges exert same magnitude (but opposite direction) charge on each other, even if charges are not equal magnitude; ex: Fab = Fba (opposite directions tho)

Pre-lecture 2a -Coulombs law? +F12 force is a force? -If q1 and q2 have the same sign? -if q1 and q2 are different signs? -R12 is equal in magnitude and opposite in direction from R21 and thus, according to newtons third law, F12 is?

-Coulombs law --> in pic; equal and opposite force is present (Newtons third law --> in pic), that is if F12 exists than F21 also must exist! -F12 force is a force by 1 exerted on 2 (shown in pic), thus F21 is force by 2 exerted on 1 -If q1 and q2 have the same sign the force is repulsive (q1 and q2 product is +) the force will be pointing outside of the 2 charges (along r12) in pic -if q1 and q2 are different signs (product of q1 and q2 is -), the force is attractive and the force will be pointing between the 2 charges (along minus r12) in pic -R12 is equal in magnitude and opposite in direction from R21 and thus, according to newtons third law, F12 is equal in magnitude and opposite in direction of F21 in pic (next slide)

-Defibrillator? -Question example +How much charge is stored by a 80 uF capacitor when fully charged to 2500 V? --> In pic (Actually a good amount of stored charge!) +How much energy can a defibrillator with this capacitor deliver?

-Defibrillator essentially a capacitator charged by a high voltage source that then releases its stored potential energy to a persons heart -Question example +How much charge is stored by a 80 uF capacitor when fully charged to 2500 V? >In pic (Actually a good amount of stored charge!) +How much energy can a defibrillator with this capacitor deliver? >Use any of 3 identical expressions all 3 will give an identical result >In pic (250 J is about equal to the KE of a 1 kg brick that has fallen from a height of 25 meters (or about 6 stories) defibrillator delivers quite a punch! (AHA, American heart association, recommends a defibrillator delivers bw 40 and 360 J of energy)

-Dielectric material that is both an? +If dielectric other than air is placed bw the plates of a capacitor? +If a material with polar molecules is placed bw the plates the electric field orients those molecules so that? +In pic +If material with nonpolar molecules is placed bw the plates the electric field will? +In either case (dielectric with polar or nonpolar molecules) the result is that just inside the? + In pic >The effect of these extra layers of charge is to? >In pic -this (dielectric) has the effect of increasing the? +if dielectric material is placed bw the plates of a capacitor, the capacitor can?. It also makes it easier to? situation) +in pic

-Dielectric material that is both an insulator and polarizable +If dielectric other than air is placed bw the plates of a capacitor interesting things happen +If a material with polar molecules is placed bw the plates the electric field orients those molecules so that + ends are pointed toward the - plate and the - ends are pointed toward the + plate +In pic +If material with nonpolar molecules is placed bw the plates the electric field will an induce a dipole an then attrack + charges toward the - plate and - charges toward the + plate +In either case (dielectric with polar or nonpolar molecules) the result is that just inside the - plate is a layer of + charges and just inside the + plate there is a layer of - charges created by the dielectric material +In pic >The effect of these extra layers of charge is to reduce the electric field, and as a result the voltage, between the plates of the capacitor by a factor known as the dielectric constant of the material (kappa, k) (extra layers of charge create electric field that is opposite direction of the electric field of the plates and thus reduces the electric field of the plates...) +In pic -this (dielectric) has the effect of increasing the capacitance by the same factor of kappa (dielectric constant) over air filled capacitance if dielectric material is placed bw the plates of a capacitor, the capacitor can store more charge per volt of potential difference. It also makes it easier to keep the charged plates separated (one of few instances in which nature provides us with a win win situation) +in pic

Summary -Electric and magnetic fields are used to? +Electric charge is the source of? +Electric charge can be? -Coulombs law? +Direction of force is always along the? +equal and opposite forces? -Electric charge net force is equal to?

-Electric and magnetic fields are used to describe a host of phenomena +Electric charge --> source of electric and magnetic fields +Electric charge can be + or - and thus leads to attractive (opposite charges) and repulsive (same charges) 2-body electric forces occurring -Coulombs law --> equation describing 2 body electric force bw 2 charges +Direction of force is always along the line that connects the charges (could be in either direction tho depending on if repulsive or attractive) + if F12 exists then F21 must exist too (equal and opposite forces!!) -Electric charge net force is equal to the vector sum of all the other forces acting on it (due to the other individual charges). superposition principle (in pic)

-Electric dipole consists of? +Ex? -Electric field points directly? -Electric field at point P ex?

-Electric dipole consists of + and - charge of = magnitude, separated by some distance +Ex: water molecule can be modeled as dipole - charge toward O end and + charge toward ends with H's -Electric field points directly away from + charges and directly toward - charges -Electric field at point P is the vector sum of the electric fields at that point due to the 2 individual charges go through ex!! +Draw individual field vectors at point P +Point P is same distance from each charge, so magnitude of electric field is the same for each vector! +Break into X and Y components for the vectors! +Magnitude and angle are the same for both electric charges Y component cancels to 0 +add the X vectors! Both are pushing in the same direction and thus explain why you can just add a 2 for the expression in the later pic! +in pic +Cos(theta) can be calculated based on adjacent and hypotenuse side (A/H) equals d/r in this pic +in pic +Same calculation for every point in space can describe the electric field of a dipole with field lines like the ones in pic

-Electric potential due to a point charge all points the same distance from the charge have the? name for this? +in pic -For a point charge there are any number of? each where and shape? +In 2D, shells are drawn using? +Often draw several what on figure? +in pic -Typically, equipotential surfaces are drawn so that potential difference bw each adjacent pair of surfaces is? -For point charges equipotential surfaces are more closely spaces the closer they get to? why? + In pic -electric potential and electric field are?

-Electric potential due to a point charge all points the same distance from the charge have the same voltage we call this group of points an equipotential surface +in pic -For a point charge there are any number of equipotential surfaces, each at a different potential (distance...) but all of them are spherical shells +In 2D, shells are drawn using their circular cross sections (x value of graph equals the radius on the sphere, from center of charge....) +Often draw several equipotential surfaces on a figure each at a different voltage +in pic -Typically, equipotential surfaces are drawn so that potential difference bw each adjacent pair of surfaces is the same (ex in pic difference is 1V bw each) -For point charges equipotential surfaces are more closely spaces the closer they get to the charge -> electric potential changes more quickly closer to the charge (where magnitude of the electric field is greatest) o In pic -electric potential and electric field are closely related we can describe any electric scenario using either electric fields or electric potential!

-Introduce what ideas? -basis for the normal force (between 2 surfaces)? +Normal force is really the sum? -Nervous system relies on? (ex?) -Topics?

-Introduce --> electricity, electric charge, electric behavior of materials, and Coulombs law (mathematical description of electrostatic force) -Electrostatic force --> basis for the normal force (between 2 surfaces)! (in pic) --> keeps you from falling through your chair +Normal force --> is really the sum of the electrostatic repulsive force of electrons in 2 different objects -Nervous system --> relies on electric impulses to control your body (retina-brain messages are transferred as a stream of electric impulses) -Topics --> how electric phenomena impact out daily lives, transfer of electric charge, insulators and conductors, and coulombs law (overall big ideas!)

-Question: Medical staff in an operating room who are working in an oxygen rich atmosphere must wear special shoes with soles made of conducting material instead of rubber to prevent a spark that could ignite the oxygen. Why?

-Rubber soles can accumulate a net charge as people walk and since rubber is an insulator, the charge can't move around. This concentration of charge makes a spark more likely. Conductive soles allow charge to disperse over the entire sole and into the person's body.

-Single charge creates electric field in all of? field can do what? +If charges have opposite signs they will? what happens with KE and PE? +If charges have same sign, they? KE and PE? -Calculus can be used to to calculate the work done by one point charge on another as they move electric potential energy of 2 point charges expression (in pic); again think of what the charges want to do, if the charges do what they want to do (opposites attract and same signs repel, the electric PE decreases, can almost think in terms of energy and more - being more favorable....) +In pic assumes that electric PE is = to 0 when charges are separated by infinite distance. PE is what? if same sign charges and what if opposite sign charges? -For same sign charges, electric PE is? (in pic_ -For opposite sign charges the electric PE has a? ( in pic) ·-If there are more than 2 charges present?

-Single charge creates electric field in all of space field can exert a force on a second charges particle +If charges have opposite signs they will attract. That is, they will accelerate toward each other and their KE will increase. Their PE decreases as they get closer and increases as they move farther apart (KE decreases as they move father apart...??) +If charges have same sign, they repel and accelerate away from each other, increasing their KE. PE decrease as they get farther apart and increases as they get closer to each other! -Calculus can be used to to calculate the work done by one point charge on another as they move electric potential energy of 2 point charges expression (in pic); again think of what the charges want to do, if the charges do what they want to do (opposites attract and same signs repel, the electric PE decreases, can almost think in terms of energy and more - being more favorable....) +In pic assumes that electric PE is = to 0 when charges are separated by infinite distance. PE is + if same sign charges and - if opposite sign charges -For same sign charges, electric PE is high when they are close and decreases when they get farther away (in pic) -For opposite sign charges the electric PE has a large - value when they are close, and electric PE becomes less negative (increases) as their separation increases (in pic) ·-If there are more than 2 charges present, then each pair of charges has an electric potential energy and the total electric potential energy of the system is equal to the sum of the electric potential energy of each pair of charges (in pic) -> scalar (Can be + or - but no direction -> just add numbers)

Sodium ions in water -The atoms in a water molecule form a? -If we add sodium ions to water, the force between a sodium ion and a water molecule is? -solubility properties has to do with? -H2O has what? +parts?

-The atoms in a water molecule form a chemical bond by transferring electrons from the hydrogen atoms to the oxygen, creating a permanent dipole. -in pic --> A, attractive (Na+ is attracted to the g- O side of the H2O molecule. Would also be attractive for a - ion bc it would be attracted to the g+ H's side of H2O) -polarity! (ex: H2O can dissolve ionic compounds well. + ions attracted to g- O. And - ions are attracted to the g+ H's) -H2O -> has a permanent dipole +H's side -> g- (partial -) side +O side -> g+ (partial +) side

Balloons and walls -A rubber balloon has been rubbed on a wool sweater, thereby giving it a negative charge. Why is the balloon attracted to a wall? +induced dipole?

-The charge is attracted to induced dipoles in the wall --> in pic +induced dipoles --> temporary dipoles; dipoles that only exist when some form of charge is brought next to it

Question (in pic)

-The magnitude of the positive charge is greater than the magnitude of the negative charge. the equipotential lines are closer together in the + charge than they are in the - charge (and difference in potential between adjacent lines is the same, ex: bw each set of lines could be 1 V)

-as is indicated in previous slides, Coulomb's law is hard to see in? +But it can be seen in operation pretty clearly at? · -Coulomb'slawcanbeusedtoexplainwhyelectrons? -Just as an exercise, let's pretend that electrons orbit the nucleus, finding its velocity ex?

-as indicated in previous slides, Coulomb's law is hard to see in the messy macroscopic world, that is the world of human scale things. This is one of the reasons it took so long to verify. +But it can be seen in operation pretty clearly at the very small scale, nearly the smallest, in fact, where charges are close to their most basic elements. -Coulomb's lawcanbeusedtoexplainwhyelectronsorbittheatomicnucleus,justlikeNewtoniangravitationcanbeusedtoexplainwhytheplanetsorbitthesun.Onefortheverybigandonefortheverysmall.Youmayalreadyknowthattheplanetarymodeloftheatomisn'taccurate.We'llseewhylaterinthesemester.ButtheforcethatkeepstheelectroninorbitaroundthenucleusisstilldescribedbyCoulomb'slaw. -Just as an exercise, let's pretend that electrons orbit the nucleus, in this case, the hydrogen nucleus composed of a single proton, just like planets orbit the sun. Since we can calculate the force on the electron, we can find its orbital velocity. Here's the expression for finding the force in the electron (IN THIS SCENARIO THE Fcentripetal EQUALS THE Fcharge) o Recall, that any object in uniform circular motion, the electron with mass M sub e is experiencing a net centripetal force, given by this expression, which means that M sub e times v squared divided by r is equal to k, the Coulomb constant, times e squared divided by r squared. Solving for v, we get v is equal to the square root of k times e squared divided by m sub e times r. +Coulomb's constant k is 9 times 10 to the 9 Newton meters squared per Coulomb squared. The fundamental charge e is 1.6 times 10 to the minus 19 Coulombs. The mass of the electron m sub e is 9.1 times 10 to the minus 31 kg. Finally, the radius of an electron's orbit in the planetary model of hydrogen r is 5.3 times 10 to the minus 11 meters. Putting all that together we get 2.2 million meters per second in other words really fast. look in pics for ex of finding velocity of electron in orbit! +in pic!

ASK -HW2 problem 10

-cosign theta idea?? +would it be different if the be had - charge because earth has - (field going toward it) and thus moving - bee away would be a decrease in potential energy??

Proportional reasoning with Coulomb -How does the magnitude of force on q1 compare in case A and case B? (in pic) +explain?

-in pic -> B +basic reasoning with equation!

Proportional reasoning with Coulomb -How does the magnitude of force on q1 compare in case A and case C? -> in pic +explain?

-in pic -> C +basic reasoning with the equation

Adding forces as vectors -The net force on q 3 is the sum of two force vectors. This sum is best represented as: +explain? -electric dipole? +external charge and polarizing?

-in pic -> D +F2on3 has a greater magnitude than F1on3 bc q2 is closer to q3 than q1 is -electric dipole -> = and opposite charges separated by some distance +external charge (could be actual charge or dipole of sorts) can polarize neutral object --> attract!

Dipoles and forces -Which best describes the net force between these electric dipoles? -> in pic +explain? +could do what here? -Which best describes the net force between the dipole and the wall? -> in pic +explain?

-in pic -> attractive (weak attraction due to distance separation... and opposing forces) +diagrams in pic --> Fnet (attraction, on left in pic) is greater than the Fnet (repulsion, on right in pic) and thus there is overall attraction -> in pic +could solve this whole problem using Coulombs to calculate each force --> would take a long time! -in pic -> attractive (also pretty weak attraction due to distance separation... and opposing forces) +same explanation as above --> diagrams in pic --> Fnet (attraction, on left in pic) is greater than the Fnet (repulsion, on right in pic) and thus there is overall attraction +induced dipole in wall is attracted to electric dipolein

Question; Question Suppose the distance between the plates of a parallel‑plate capacitor is increased without changing the amount of charge stored on the plates. What will happen to the energy stored in the capacitor? ask about!!

-it increases + The capacitance 𝐶C of a capacitor is determined by the geometrical properties of the capacitor's plates and the material between them. For a parallel-plate capacitor without a dielectric, the capacitance is determined by the constant 𝜀0ε0 , the area 𝐴A of each plate, and the plate separation distance 𝑑d . 𝐶=𝜀0𝐴/d Because 𝐶C varies inversely with 𝑑d, increasing the plate separation decreases the capacitance. The potential energy 𝑈electricUelectric stored in a capacitor is related to the magnitude of the charge 𝑞q on each plate and the capacitance 𝐶C . 𝑈electric=𝑞^2 / 2c The charge 𝑞q remains constant while 𝑑d increases and 𝐶C decreases, therefore the energy stored in the capacitor 𝑈electricUelectric increases. This result is understood in the context of work. Because each plate is oppositely charged and electrically attracted to the other plate, work is required to further separate the charges. The energy supplied during the work done on the capacitor is then stored in the capacitor in the form of electric potential energy. Think -> plates are opposite charge and thus want to be together --> moving them apart is unfavorable and thus results in an increase in energy (work is done to move them apart)

-positive point charge has electric field lines? equipotenital surface? +Electric potential surfaces are (Always)? >explain? (in pic) +If we move in the direction of an electric field line, the electric potential?. If we move in opposite direction of electric field line electric potential? true for both? >For +? >For -? >Electric field lines always point in the direction of? (in pic) -If we have a uniform electric field, we can relate the change in electric potential to the? +d is the? +theta is angle of? +in pic -Use similar ideas, but with calculus if electric field?

-positive point charge has electric field lines pointing away and equipotential surface is spherical +Electric potential (equipotential) surfaces are (Always) perpendicular to the field lines >Consider work and energy since electric potential is potential energy per unit charge if we place a small test charge anywhere on an equipotential surface, the potential energy will be the same electric field cannot do work on the test charge as long as it remains on the equipotential surface only way the electric field could do no work on the test charge is if test charge always move perpendicular to the electric field (in pic) +If we move in the direction of an electric field line, the electric potential decreases. If we move in opposite direction of electric field line electric potential increases true for both + and - charges >For + move in direction of field, become smaller + number. and move opposite direction of field become larger + number >For - move in direction of field and become larger - number. and move opposite direction of negative field and become smaller negative number >Electric field lines always point in the direction of decreasing electric potential (decreasing could mean smaller + number of a larger - number) in pic -If we have a uniform electric field, we can relate the change in electric potential to the electric field (similar to how we relate potential energy to work done on charge) equation in pic o d is displacement of charge in electric field o theta is angle of displacement relative to the electric field direction in pic -Use similar ideas, but with calculus if electric field is not uniform

-Question: Consider a rubber rod that has been rubbed with fur to give the rod a net negative charge, and a glass rod that has been rubbed with silk to give it a net positive charge; After being charged by contact by the fur and silk,

-the rubber rod has more mass and the glass rod has less mass. --> electrons have mass (- charge gained elections and + charge lost electrons)

Pre-lecture 2b -All charges have? +Electric field permeates and modifies all? -Measuring electric field of a charged particle +process with test and source charge? +Test charge has different force exerted? +If magnitude of source charge changes? -If source charge changes sign, then the direction of the electric field its creating is? +Field direction with + and -? -Electric field is a what quantity? -SI Units of electric field are? -If more than one source charge creates an electric field electric field at any point is the?

-· All charges have an electric field associated with them +Electric field permeates and modifies all space -Measuring electric field of a charged particle +Put source charge (want to measure field) by test charge. Measure the force exerted by the source charge on the test charge using Coloumbs law; Q is source charge and q is test charge +Test charge has different force exerted on it at every point in space electric field (of source charge) can be different at every point in space +If magnitude of source charge changes magnitude of the field it creates changes to +If source charge changes sign, then the direction of the electric field its creating is reversed (generally assumed that test charge is +). +Field goes away from + source charge and towards - source charge. (in pic) -Electric field is a vector quantity has magnitude and direction, just like force (equations in pic!) -SI Units of electric field are N/C (Newtons/Coulomb) bc force is in N and charge is in C -If more than one source charge creates an electric field electric field at any point is the vector sum of the electric field from each individual (source....) charge (vector addition and subtraction and what not!) --> in pic next slide

Prelecture 3a -Electric potential ? +Electric potential related to electric potential energy equation? -Electric field electric force per unit charge +E? +Need single charge to make an? +But need 2 charges for an? -Only single charge is required to create an? +2 charges are required to have an? +in pic -Mathematically, we write the electric potential for a point charge by? -Negative charge? +Positive charge? +Magnitude of electric potential is? +Much like potential energy, the precise value of electric potential at any point in space is? +equation for electric potential? -Important quantity? +Potential difference measured in? -Units of volts can be written in? +Generally, when computing the electric potential due to individual charges assume that? -If several point charges are present? +Electric potential is what type of quantity?

-· Electric potential electric potential energy per unit charge +Electric potential related to electric potential energy (in pic) -Electric field electric force per unit charge +E = F/q +Need single charge to make an electric field +But need 2 charges for an electric field to be exerted -Only single charge is required to create an electric potential +2 charges are required to have an electric potential energy (in pic) -Mathematically, we write the electric potential for a point charge by dividing the electric potential of that charge and a small test charge by the test charge o in pic -Negative charge negative electric potential (in pic) +Positive charge positive electric potential +Magnitude of electric potential is large close to the charge and goes to zero infinitely far from the charge +Much like potential energy, the precise value of electric potential at any point in space is rarely important +equation; V=kQ/r -Important quantity potential difference (in electric potential) (Delta V) bw 2 points in space +Potential difference often measured in volts (V) potential difference is often referred to as a voltage -Units of volts can be written in a variety of ways +Generally, when computing the electric potential due to individual charges assume that electric potential is 0 infinitely far from the charges (r infinity and V 0) -If several point charges are present the electric potential at a given point is calculated by adding the electric potential at the point due to each of the individual charges (in pic) +Electric potential scalar quantity (Can be + or - but there is no direction associated with it!) just add numbers together

Pre-lecture 1 -mechanics? -kinematics? -newtons laws? -conservation of energy and momentum help us understand? -apply all of the above ideas to? -· All matter has? -Charge on 2 objects results in? +often useful to think of these forces in terms of? -Electric forces (and resulting motion of charges and conduction material) lead us to? -Electric + magnetic fields lead to? -Will briefly explore what at end of course?

-· Mechanics --> physics of motions of objects (s, l, g) -Kinematics --> describes how objects translate from one location to another -Netwons Law --> tools for describing an objects acceleration -Conservation of energy and momentum --> help us understand the evolution of a system from one state to another -Apply all these old ideas to charged objects!! (in pic!) -· All matter has electric charge (just like it has mass) -Charge on 2 objects --> results in the objects exerting electric and magnetic forces on each other (primary focus of this course) +often useful to think of these forces in terms of electric and magnetic fields, which modify all of space -Electric forces (and resulting motion of charges and conduction material) --> lead us to explore circuits (electric forces circuits) -Electric + magnetic fields --> leads to exploration of light and optics -Will briefly explore modern physics at end of course

Question: A parallel‑plate capacitor has a potential difference 𝑉0 between its plates. If the potential difference is increased to 2𝑉0 , what effect does this have on the capacitance 𝐶?

-𝐶 remains unchanged + capacitor is a device that can store electric charge. Capacitance is the electrical property of a capacitor that describes how much charge it can store when held at a given electric potential difference (i.e., voltage). The capacitance of a capacitor depends only on the geometry of the capacitor's plates and the material between them. For a parallel-plate capacitor without a dielectric, the capacitance is determined by the constant 𝜀0, the area 𝐴 of each plate, and the plate separation distance 𝑑 . 𝐶=𝜀0𝐴/𝑑 Increasing the potential difference between the plates does not affect the area of the plates nor their separation distance, therefore 𝐶C remains unchanged. Capacitance is analogous to the spring constant of a spring, which is determined by the physical characteristics of the spring and not by how much mass is attached to it. (be careful NOT to misuse q=CV)

There are two ways of drawing the distribution of charge in objects, and you'll want to be able to determine which you are looking at or being asked for. -One kind of drawing depicts the? practical? +ex? -Another way to say this? and other way to draw? +ex? (in pic) -One of the biggest clues to determine what kind of picture you're looking at is - There is one case in which drawing excess charge doesn't really help? explain?

Because we'll be talking a lot about electric charge and materials, you'll encounter lots of pictures of how charge is distributed in objects. There are two ways of drawing the distribution of charge in objects, and you'll want to be able to determine which you are looking at or being asked for. -One kind of drawing depicts the total/actual charge in an object, at least in principle. Most ordinary solid objects have huge amounts of charge in them, so actually drawing out all the positives and negatives isn't practical. +There are, for instance, 10 billion, billion, billion positive and negative charges in the average human. With numbers like that, there's no way we can draw every charge. But we could draw a bunch of charges just to indicate there are positive and negative charges scattered throughout. --> This picture tells you in broad strokes what you'd find if you looked at a person on the atomic scale. However, as in most macroscopic objects, these positive and negative charges are essentially all paired. So on the whole, the average human body is electrically neutral. -Another way to say this is that a person is electrically neutral when you look at the big picture. We can thus draw a slightly different image, one that takes this bigger perspective. In this case, we would only draw any excess/net charge in a person, that is, any charge that isn't balanced in its immediate location by charge of the opposite sign. If there is no excess charge, then we just draw a blank picture to indicate that the person is, again, on the whole, electrically neutral. +Let's look at an example. Suppose we have a solid object made of a conducting material that has charges in it at the atomic scale, like all solid objects, but in which those charges are all paired. We then bring a rod made of an insulating material with an excess positive charge close to that object. You might have guessed that this rod will attract all the negative charges, in this case, mobile electrons, leaving behind positive charge, atomic nuclei that aren't fully paired with an equal negative charge. --> What will this look like if we just draw the excess charge on the object? In that case, the drawing of the object starts blank since the net charge everywhere is zero. But when charge moves around, it's no longer paired everywhere. Now there is more positive charge on the right unpaired with negative charge and an excess of negative charge on the left. (Note that throughout, we've only been drawing the excess charge on the rod made of insulating material) -One of the biggest clues to determine what kind of picture you're looking at is whether the reference is made to total or to excess charge. Which word gets used will tell you what kind of picture you're looking at or need to draw (in pic) -There is one case in which drawing excess charge doesn't really help, namely when an object made an insulating material is exposed to external charges (in pic) Here, the insulator starts out like all other electrically neutral objects. Positive and negative charges are all present, but cancel one another out._When you bring an external source of charge nearby, charges do not move any large distance inside the insulator. Instead, there is a slight separation of positive and negative charges on the atomic scale. Inside the molecules that make up the object, electrons are pushed to one side. This creates lots of tiny dipoles. Now we'll talk more about dipoles next time, but for the moment you just have to recognize that this very tiny separation of charges can create attractive forces you can actually see in action, for instance, the magic of sticking balloons to walls.

Charges in fluids behave differently than? implications? -how do charges move in a solid? why? -how do charges move in liquids? -why is this difference important? -cell boundary ex of ion importance? -neuron importance of ion ex?

Charges in fluids behave differently than charges in solids, and this has some big implications for biology. -When charge moves in a solid, it's in the form of electrons, because electrons have low mass compared to atomic nuclei and can be weakly bound to those nuclei and therefore mobile. Meanwhile, the nuclei themselves are linked together to form a solid structure. -In fluid, things are much more, well, fluid. Charge typically moves in the form of ions, whole atoms that have a net negative or positive charge because of an electron deficit or surplus. Recall that this is the case for water. -in solids -> only electrons (- charges) can really move around (ex: conductors electrons move well and insulators electrons dont move well) +in liquids -> both + and - charges (ions) can move around! -The importance of ions in fluids is particularly clear if we look closely at a cell boundary. Outside of a cell, there are typically more positively charged ions. Inside a cell, there are typically fewer positively charged ions. This means that there is a charge gradient across the cell boundary-- that is, a transition from fluid with a net positive charge outside the cell to a fluid with a net negative charge inside the cell. --> The cell boundary has to work to create this gradient. It does this work using ion pumps that move ions across the cell boundary. -The motion of ions across a cell boundary is the means by which neurons send signals to other neurons in the body. Like other cells, the fluid outside the axon of a neuron normally has a net positive charge, while the fluid inside the axon has a net negative charge. When the dendrites of the neuron receive a chemical signal from another neuron, ion gates in the part of the axon closest to the neuron's nucleus open up. The first gates move positively charged sodium ions inside. This creates a reversal of the normal charge gradient across the cell boundary. The reversed charge gradient in one part of the axon causes ion gates in the adjacent part of the axon to open. While the original segment returns to normal, the charge gradient next door reverses.Now, th e reverse charge gradient causes iron gates to open down the line. The same cycle repeats all the way down the axon until the reverse charge gradient reaches the end of the axon, causing the neuron to send a chemical signal to the next neuron, where the whole process happens again.

How does the Gecko do it? Geckos can climb smooth surfaces like glass. Which of the following best describes how this is possible? -dont need what to attract? +neutral objects can? +charged and neutral?

Electric dipoles in their feet are attracted to induced dipoles in the glass --> 2 (overall/net) neutral objects attract here! -dont need charged objects to attract +neutral objects can attract other neutral objects --> dipoles (and vanderwall interactions) +charged and neutral objects can attract to

Electrical categories (many materials fall in one of these 2 categories) --> only what can move in conductors and insulators? -Insulator +Charges are? +Ex? +Charges in insulators are? +Ex: electrons remain in? -Conductors +Charges can? +Ex? +Repulsive forces? -Electric charges are generally carried by what in biological systems? +Water is? +Ions are attracted to H2O flow?

Electrical categories (many materials fall in one of these 2 categories) --> only electrons (- charge) can really move in both conductors and insulators (solids!) (+ charges are essentially trapped and move very little due to lattice structure... protons?) -Insulator +Charges are not free to move within the material (atomic structure doesn't allow it) +Ex: glass and plastic +Charges in insulators are essentially fixed +Ex: electrons remain in place on a rubber rod and don't move throughout it (in pic) --> repulsive force occurs between the charges (Same sign charges) but rubber exerts and equal and opposite force on the charges that prevents them from accelerating (moving to different parts of rod) -Conductors +Charges can move freely within the material (allowed by the atomic structure) +Ex: metals and H2O +Repulsive forces between charges (Same sign charges) cause the charges to distribute around the surface of the conductor (in pic) -Electric charges are generally carried by ions in biological systems (H2O becomes important!) +Water is electrically neutral but is polar and has a partial + by the H's and a partial - by the oxygen -Ions are attracted to H2O (ex: -Cl is attracted to g+ H's and +K is attracted to g- O) --> H2O molecules with the ions "attached" to them are free to move --> H2O is a good conductor as it moves these ions! (water helps + and - charges move in the body by doing this!)

Example 3 point charges all with same magnitude -Zero of electric potential at r? -Electric potential scalar so? -Just add the? +in pic -Check to make sure answer makes sense?

Example 3 point charges all with same magnitude -Zero of electric potential at r=infinity -Electric potential scalar so sum is just a math sum (Add numbers!) no vectors to worry about -Just add the three terms together! + in pic -Check to make sure answer makes sense this answer makes sense bc it is + and then two closest charges are both + and the contribution of electric potential from each charge decreases (by 1/a) as size of square increases!

If a substantial enough excess charge builds up on a material, then under certain circumstances, that charge can? (charge basically wants to?) -charge on insulator ex? -charge on conductor ex? ·One way to prevent the build-up of excess charge on objects is called? -An object is grounded when? +It turns out that connecting an object to the Earth? >If you connect a positively charged object to the Earth? >If you connect a negatively charged object to the Earth? >You don't need the entire Earth to? idea? +relate to thermodynamics idea and fluids ideas? >fluid metaphor fun facts? .

If a substantial enough excess charge builds up on a material, then under certain circumstances, that charge can leap off in the form of a spark (charge basically wants to spread out to be at equal concentration in different areas!....) -Suppose we place a large negative charge on a particular spot on an insulator. This charge won't move, given the nature of insulating material. --> Now we bring another object with less negative charge close by, but not touching. If the gap is small enough and the charge difference is great enough, a surge of charge will jump from one object to the other (in pic) -In a conductor, remember that charges can move freely. This means that if there is an excess charge on the conductor, all the excess charge moves to (throughout) the surface. The density of charges- that is, the number of charges per unit area- will be particularly high on sharp points. Once again, if we bring another object close, there can be a spark as charge moves between the two. (in pic) -One way to prevent the build-up of excess charge on objects is called "grounding." +An object is grounded when it is connected to a very large neutral object that can absorb any excess charge without much trouble. +It turns out that connecting an object to the Earth is an excellent way of getting rid of excess charge, hence the term "grounding." >If you connect a positively charged object to the Earth, electrons will rush into it because of their attraction to positive charge. >If you connect a negatively charged object to the Earth, electrons will rush out of it because of their mutual (electron to electron?) repulsion. >You don't need the entire Earth to ground an object. For a small object with a slight excess charge, you can ground it simply by touching it. The charge that moves into or out of your body really doesn't make that much difference. +You've already seen a phenomena very much like this, like grounding, in a very different context, namely thermodynamics. --> We sometimes spoke of placing an object in contact with a thermal reservoir that would absorb or release heat energy, but not change temperature. Imagine you jumping into the ocean. If you're hot, it can cool you down. If you're cool, it can warm you up. But the temperature of the ocean doesn't change much in either case. --> In a similar way, you can imagine an object you use to ground another object as an ocean of charge. +The fluid metaphor here isn't totally random. Once upon a time, charge was believed to be a fluid. There was one fluid for positive and another fluid for negative. This was the prevailing belief when Ben Franklin sent up his kite. --> At the same time, heat was believed to be another kind of fluid called "phlogiston." This particular theory of heat was called "caloric theory" from whence comes the modern word "calorie." We'll return to fluid metaphors to understand electricity later in the course.

Gecko Foot structure -key structure in their feet?

In pic -Setae --> dipoles exist in these (tiny spatula like things..??)

Let's take a closer look at the similarities and differences between Newton's law of gravitation and Coulomb's law. -Gravity is always attractive? +Coulomb forces can be? +The existence of both kinds of charge is the reason why? -Gravity experiences inverse? +The Coulomb force experiences inverse? -Gravity is a what force? +Coulomb force is a what force? +Recall that a conservative force is one that? -Gravity is weak compared to? +It may seem like gravity is the? +However, the existence of two kinds of charge means that, on the whole? · The fact that both Newtonian gravity and the Coulomb force are apparently governed by inverse square laws is more than just a curiosity. -It also makes available, a powerful problem solving tool called? +ex:?

Let's take a closer look at the similarities and differences between Newton's law of gravitation and Coulomb's law. -Gravity is always attractive-- that is, masses are always pulled toward each other. +Coulomb forces can be attractive-- opposite charges-- or repulsive-- same charge. This is a very big difference. +The existence of both kinds of charge is the reason why matter, on the whole, is electrically neutral. And why electrical forces don't generally play an obvious role in everyday life. There is no matter with antimass so gravity is never weakened by antigravity. -Gravity experiences inverse square change with distance. +The Coulomb force experiences inverse square change with distance. This similarity, coupled with general reverence for Isaac Newton, is one of the reasons why some people were very happy with the law that Charles-Augustin de Coulomb proposed in the late 1780s. Even though his experimental results were questionable, many decades of subsequent experiments eventually showed he was right. -Gravity is a conservative force-- that is, total energy is always conserved. And change in total energy over any closed loop is 0. +Coulomb force is a conservative force-- that is, total energy is always conserved. And change in total energy over any closed loop is 0. +Recall that a conservative force is one that conserves energy in a system, unlike friction which removes energy. We already know gravity is a conservative force. Not surprisingly-- because it has the same mathematical form-- so, too, is the Coulomb force. We'll be talking more about this next week. -Gravity is weak compared to electricity. Electricity is strong compared to gravity. +It may seem like gravity is the greater force, it's holding you down right now. But electrostatic forces are actually stronger. The electrostatic forces between molecules are keeping you from falling through the floor. +However, the existence of two kinds of charge means that, on the whole, electrostatic forces-- like the Coulomb force-- are felt only over short ranges. The bigger we make r, the more positive and negative charges will cancel each other out (more charges introduced that can cancel over larger distance?) · The fact that both Newtonian gravity and the Coulomb force are apparently governed by inverse square laws is more than just a curiosity. -It also makes available, a powerful problem solving tool called proportional reasoning. If we have a certain source-- either mass or charge-- then we can determine how the force it exerts on another object will change as the distance between them changes, even if we know nothing else about the masses or charges. Example below +Suppose we have two positive charges at some distance, r, from one another. There is some neutral force of repulsion, but we can't calculate it without any numbers. Now imagine we double the distance between the charges. We still don't know the force they exert on each other, but we can say how much this force changes. +In the original case, we know the force between the charges was given by this equation. We know the forces between the charges then becomes something given by this next equation. If we simplify, we see that the new force is 1/4 the original force. In other words, if we double the distance, we change the forces between the charges by 1 over 4. +What do you imagine will happen if we triple the distance between the charges? Or halve it? Triple -> 1/9 the original charge. ½ -> 4x the original charge.

Mapping electric field of point charge -Electric field vectors always point away from? and have? -If we connect the electric field vectors together? +lines always point in direction of the? +field lines are just? -Electric field lines spacing and strength? ex? - Electric field extends in all? -If charge creating the field is negative, the field lines point toward the (negative) source charge bc that's the direction of the force on the + test charge. If the charge creating the field is positive, the field lines point away from the source charge bc that's the direction of the force on the + test charge (based off the assumption that test charge is positive idea....)

Mapping electric field of point charge -Electric field vectors always point away from a + charge and have a smaller magnitude farther from the + charge -If we connect the electric field vectors together create electric field lines (lines are combo of all the field vectors in space) +lines always point in direction of the electric field at that location +field lines are just representations and the electric field exists in areas that don't have lines shown too! (in pic) -Electric field lines are spaced farther apart in regions where the electric field is weaker; ex: field lines get farther apart as you get farther from the point source charge because the electric field is weaker farther from the source charge. Electric field is stronger where the field lines are closer together; ex: close to the source charge and lines are closer together (in pic) -Electric field extends in all directions (3D) -If charge creating the field is negative, the field lines point toward the (negative) source charge bc that's the direction of the force on the + test charge. If the charge creating the field is positive, the field lines point away from the source charge bc that's the direction of the force on the + test charge (based off the assumption that test charge is positive idea....) (in pic next slide)

Review -in pic electric potential is measured in volts -Often speak of electric potential at given point important to remember that we always measure a? +Electric potential at a specific point is measured relative to a point? >in pic -Electric fields and electric potentials are? -Equipotential surfaces? always perpendicular to? § In pic

Review -in pic electric potential is measured in volts -Often speak of electric potential at given point important to remember that we always measure a potential difference +Electric potential at a specific point is measured relative to a point infinitely far away where the electric potential is 0 in pic -Electric fields and electric potentials are closely related -Equipotential surfaces surfaces in which electric potential is the same everywhere; equipotential surfaces always perpendicular to electric field lines! § In pic

So how do we charge up a capacitor? For simplicity's sake we'll continue to focus our attention on the parallel plate variety. -One thing is for sure, we do not?. +The whole point of the capacitor is to keep positive and negative charges? -Charge will only move directly from one plate to another when there is? +This is basically the cause of? +In pic Back to our parallel plate capacitor. How do we get the positive and negative charges on the plates? -The best way is to hook them up to some sort of? +The charge doesn't want to move this? +In pic -One not very useful way to discharge the potential energy stored by a parallel plate capacitor would be to? +Rather, we can disconnect the battery and connect the two plates to some device with? +In pic

So how do we charge up a capacitor? For simplicity's sake we'll continue to focus our attention on the parallel plate variety. -One thing is for sure, we do not move charges through the gap between the two plates. +The whole point of the capacitor is to keep positive and negative charges separate, despite the attractive force between them, thus creating some stored potential energy. -Charge will only move directly from one plate to another when there is a dielectric breakdown, that is when so much charge accumulates on the plates that the material in the gap (becomes conductive and lets charge flow through...?) between them can't keep all those charges separate. This results in a spark as charges rapidly leap the gap and all the stored potential energy is lost in one jolt. +This is basically the cause of lightning. As you already know, during a storm there can be a buildup of negative charge at the bottom of the storm clouds. This induces positive charge at the surface of the earth. And voila, you have a capacitor. The air can keep these charges apart until the electric field between them reaches a strength of about 3 times 10 to the 6 volts per meter. If the E-field gets more intense because of concentrations of charge, then the air breaks down and charge comes flooding down from the sky. +In pic Back to our parallel plate capacitor. How do we get the positive and negative charges on the plates? -The best way is to hook them up to some sort of charge pump. Like a water pump moves water from one location to another by creating a pressure gradient, a charge pump can move charges around by using a voltage gradient. A battery is essentially a charge pump. You may think of a battery as a source of charge, but it really just pushes charge through itself from one terminal to another. +The charge doesn't want to move this way any more than water wants to move uphill. But the battery will still keep pushing charge around until there is a voltage gap between the plates that equals the voltage gap and the battery. At that point, the battery can't move any more charge. It isn't strong enough. It can only keep the charge where it is. If you want more charge on the plates, you need a battery with a bigger voltage. +In pic -One not very useful way to discharge the potential energy stored by a parallel plate capacitor would be to let the two plates slap together, that is convert the electrical potential energy into the kinetic energy of the plates. Once they were in contact, the positive and negative charges would mix and the net charge on the plates would become zero. +Rather, we can disconnect the battery and connect the two plates to some device with conductive wires. The positive and negative charges on the plates can't get to each other, which is what they want to do, via the gap between the plates. But now we've offered them an alternative route. They'll rush through the wires and through the device. We can get them to do some work, at least, until there isn't any charge in the plates left to flow this would be like diverting a waterfall through a turbine to generate power. +In pic

The previous example is a particularly important one because it points us in the direction of something called an electric dipole. -Let's first suppose that the middle object in the picture has a charge of minus 10 microcoulombs. Now if we imagine that the two charges on the left are the two ends of a single object, we have an electric dipole. (in pic) +A dipole is, on the whole? lBut within it? -We've already seen that a water molecule is a? -The ubiquity(abundance) of electric dipoles is one more reason why? -The force that dipoles exert on other charges or other dipoles is called the? +Because it always includes components due to both the positive and negative ends, it is typically?

The previous example is a particularly important one because it points us in the direction of something called an electric dipole. -Let's first suppose that the middle object in the picture has a charge of minus 10 microcoulombs. Now if we imagine that the two charges on the left are the two ends of a single object (drawing with box around them!), we have an electric dipole. (in pic) +A dipole is, on the whole, electrically neutral, like almost all chunks of matter. But within it, equal positive and negative charges are separated by some distance. -We've already seen that a water molecule is a dipole. So are many other chemically and biologically important molecules (in pic) -The ubiquity(abundance) of electric dipoles is one more reason why, as we move beyond the atomic realm, that electrostatic forces get more complicated than the Coulomb law by itself. +The force that dipoles exert on other charges or other dipoles is called the Van de Waals force. Because it always includes components due to both the positive and negative ends, it is typically smaller and shorter ranged than the force that a single charge would exert. This is essentially, two charges shielding each other. We'll explore this more electron.

When Uranium 235 absorbs a neutron, it can undergo? -One possibility is that is splits into? -Assuming 2 nuclei start at rest and are just touching each other with to center distance of 11.8 femtometers, what is the final KE of the nuclei when they are very far apart? +Total mechanical energy of the 2 nuclei system remains? +PE is the? (in pic) +Initial KE is? +Final PE is? +So, the final total KE is = to? (in pic) · -Might not seem like a lot of energy, but?

When Uranium 235 absorbs a neutron, it can undergo fission, splitting into 2 smaller nuclei -One possibility is that is splits into 2 palladium nuclei (each with 46 protons) -Assuming 2 nuclei start at rest and are just touching each other with to center distance of 11.8 femtometers, what is the final KE of the nuclei when they are very far apart? +Total mechanical energy of the 2 nuclei system remains constant +PE is the electric PE bw the 2 nuclei which each have a charge equal to that of 46 protons (in pic) +Initial KE is 0 bc nuclei are initially at rest +Final PE is 0 because they are very far apart in the final state +So, the final total KE is = to the initial total PE (in pic) -Might not seem like a lot of energy, but a small amount of uranium has a lot of atoms which when they all fission release a lot of energy!

how do some fish create electrical fields? (How do fish create electric fields?) -what does jelly substance that allows some fish/sting ray to detect these electrical fields act like? (The gel in ampullea of Lorenzini is still something of a mystery, but there has been some research on how it works. Here is an article about one such study. (You may want to right click and open it in another window, Which of the following statements best characterizes the results of this study?)

by breathing (respirating) --> by breathing -jelly substance acts like a fluid conductors that effectively facilitates the transfer of + charge very well (protons move through it well!) --> The gel behaves like a fluid conductor and allows positive charges to move.

pic for last slide --> equal and opposite charge forces

equal and opposite charge forces!! in pic!

+ charge with fields (pics from previous slide)

in pic

- charge with fields (pics from previous slide)

in pic

H2O with ions in water pic (pic from previous slide)

in pic

Neuron firing (ion importance) --> pic from previous slide

in pic

electric field direction with + and -

in pic

example pics from last slide

in pic

pic for last slide about orbiting comparing bw electron and nucleus and planets and sun

in pic

pic from last slide; electric field addition idea

in pic

pics last slide

in pic

pics last slide -what makes something a strong dielectric?

in pic -more polarizable dielectric -> stronger dielectric bc it can create a large E to oppose the E of the capacitor --> ???? check this????..........Although I wouldn't use the term "strength" to describe it, materials with a higher dielectric constant (κ) are more easily polarized(fromspike!!)

pic for last slide; net force of charges -adding vectors method?

in pic -tip to tail! and then find angles and what not using trig and soh cah toa!

PE of charges moving with same or opposite signs graph (pics from last slide)

in pic (same sign on top) (different signs on bottom)

Important information

in pic --> Exams and other important info

104 Teaching team

in pic --> teaching staff -you are most important member of the teaching/learning staff

Weekly Learning Cycle

in pic --> weekly learning cycle -TA is there to help at the help desk on fridays! -quiz is open thursday and due sunday --> have 24 hours to complete it once you open it

Weekly Learning Cycle

in pic --> weekly learning cycle -prelecture and bridge are for participation -homework is on achieve -quiz is on canvas

Question --> in pic, explain?

o Points straight down the x vectors cancel out (pulling in opposite directions!) and just the Y remains going straight down

Question Two electric charges are 15 cm away from each other. If you change the distance between them to 5 cm, what happens to the force they exert on one another?

o The force increases by a factor of 9.

-Ex of using coulombs law; adding together forces (Vectors) to get a net force!

· Ex of using coulombs law; same sign charges will repel so in the ex it would be + in the X direction (F1on3). Opposite charges will attract so in the ex it would be - in the x direction (F2 in 3). The net force ends up being in the - X direction bc although q1 has a greater magnitude than q2, q2 is much closer to q3. Consider the equation and the fact that r is squared! -in pic