Okay, we're going to go back now, take another look at Coulomb's Law, and talk about an idea of, the idea of an electric field. So, let's take another look at Coulomb's Law. And let me just remind you, first of all, if I have two charges, Q1 and Q2 separated by a distance r, there's going to be a force between them given by Coulomb's Law. The product of the charges over the square of the distance, times this constant k. And, so now what I want to do is, introduce the idea of an electric field. And we can do that really, just by rewriting Coulomb's law. So if I take one of the charges out of this formula, factor it out and put it in front. And then write the remaining part here that is something we can call the electric field produced by the charge q2. And so this E2 is k q2 over r squared. Now, so we can think of this charge q2 as being surrounded in space by something that we're going to call the electric field. And I've drawn, really the lines of force of the electric field that show the, this is the direction of the electric field, that's positive if this is a positive charge its pointing outward. and so now we can think of the other charge q1, as being placed in the electric field of q2, and then I can compute the force on q1. It's just the charge of q1 times the electric field produced by q2. And that is the exact same force as Coulomb's law told me, but now I'm just looking at it a slightly different way. I'm saying okay, part of the factor here is the electric field of charge q2. And then q1 finds itself experiencing a force, because it's feeling the presence of q 2 through the electric field, that q2 has produced. Now of course you could do this the other way. You could say, okay, I'll compute the electric field of q1, and then say, I'll place q2 in the electric field of q1, which is e1. And then I calculate the force as q2 times e1, the field of, of the, the first charge. And that is, of course, the same formula as the original Coulomb's law. So you can really think of for our purposes, you can really think of the electric field as just kind of a convenient way of looking at Coulomb's law slightly differently. Now of course just to sum this up, the force that you com, that you compute doesn't matter if I say okay, I'll compute the electric field of a charge q1, and then the force on charge q2, that's, that expression. Or I can compute the electric field of charge q2. And then compute the force on q1 by multiplying E2 times q1. It comes out the same in both cases. Okay. So now, [COUGH] let's take a look, instead of just looking at point charges, let's look at the electric field between two charged plates. Now, where we're going with this, is we want to introduce the idea of voltage and potential difference. Now, [COUGH] let's say I have two plates, two metal plates. And I put a plus charge on one plate, plus q, and a negative charge on the other plate. there's going to be an electric field, that goes from the positive charge to the negative charge. And if the plates are very large, then the field inside the plates is uniform and pointing plus to minus. And, [COUGH] so now let's say I'm going to put a charge, a little test charge q, somewhere in between those plates. Now there's going to be a force on this test charge q, that's its charge times the electric field. Now, we have to go back and look at some of the ideas from basic physics, and be very clear about the, the difference between work and energy and power. Now, work and energy are the same thing. Now, to move the charge against the electric field, or the force that the electric field's producing, requires that we do work on that charge. So think of it as, i, i, imagine you're holding this charge with your your fingers somehow, and it, there's going to be a slight force. It's a positive charge pulling it toward the minus q plate. So imagine we took and we pushed the charge the other way toward the plus q plate. So there's a force pushing back, and so we have to do work, or we have to exert energy, to move the charge counter to the direction that the electric field would like to push it. Now as I said, work is force times distance. That's from basic physics, the definition. And so work, as I said, which is is units of energy, is force times distance. So imagine just a little analogy back from high school physics hopefully. I have a mass that is sitting on an incline plane. And there's a component of the force pushing back down the plane. which is the, the mass times the acceleration of gravity. So that's the weight of the object times the sine of this angle. And so if I wanted to push on this block, and push it up the plane, the distance d, I have to do work. And the amount of work that I have to do is the force, mg sine theta times the distance that I've moved the block. So it requires energy to move the block up the plane. Now [COUGH], going back to the electric charges. Let's say I have a electric field pointing to the right, and I have a plus charge placed in that electric field. There's going to be a force on that charge, which is q times E. And so the force is positive and pointing to the right. So now let's say that the, so in this point the electric field is trying to move the charge. And lets say that the charge is moved by the electric field the distance d. Then the work done, by the electric field on that charge, is the force times distance. So it's qE times d. Now that's a positive number. That means that the electric field is doing work on the charge. It's adding energy to the charge. So you could imagine, let's say I, I put a little bit of Styrofoam with some plus charge here. A little piece of plastic with some plus charge on it. And I [COUGH] put that in, in a region of space where there's an electric field. It's going to be accelerated to to in the direction of the field. And so it's, if it's accelerated through this distance d, the electric field is adding energy to it. And so when it gets over here it's now moving. It, there's I've, there's kinetic energy of this particle, which is equal to the amount of work that the electric field has done on that particle. Now [COUGH] imagine I put a negative charge in this same electric field. Well the electric field would like to push the charge to the left. If I force the charge to move to the right, I have to exert a force to move the charge in that direction. And so in that case the the, the work is minus q, this charge, times E, the electric field, times the distance that I move it from left to right. Now that comes out to be a negative number. That means that we had to do work to move the charge. Okay, now that brings us to the idea of electric potential, or voltage. Now [COUGH] back to the same picture. If I'm trying to move a charge if I move it, letting a charge move through a along the direction of an electric field. Let's go back and think for a second. That electric field would've been produced by segregating some plus charge and negative charge like this, like imagine these were two plates, and I put plus q on that one and minus q on that one. Now, the charge is moving in the direction of the E field force in this case, and the E field is doing work on the charge, it's adding energy. So what we're saying, is that the charge moves from a higher potential to a lower potential. So over here, there's a lot of potential energy. Over here there's less potential energy, and so, and that's been converted to kinetic energy of this moving charge. Now [COUGH] If I go back and look at that previous picture with the negative charge. And the, so I have, if I put a negative charge down, and an E field pointing to the right, there's a force pointing to the left because minus q times E is a negative number. And then if I move the charge over from here to there, to the right, at distance d. I have to do work against the electric field force, to move the charge. So I have to expend energy. And so, this is starts at a point of lower potential, and I'm moving it to a point of higher potential. So, in general we can, generalize that notion. And just say okay, I'm going to not think about the electric field itself. But, I'm going to just talk about the electric potential as having different values in space. And the change in potential is all that matters. So, if I go from a region of high potential to low potential, there's a potential difference in delta V. [COUGH] And that tells you the, enables you to calculate the work that the electric field would do to move a charge from potential V2 to V1. And that amount of work is this q times this potential difference. And that is q times V2 minus V1. Okay so let us sum this up with some the conclusions from this. So if a positive charge moves through a potential difference from V2 to V1, where V2 is bigger than V1, the electric field does work on the charge. It adds energy to the charge. The charge would like to move that way, and if I put it down it zips along, picks up some kinetic energy, because the electric field pushed the charge in that direction. Now here's the potential diagram version of, of the, saying the same thing. If a charge starts off at a high potential, it can drop to the lower potential and acquire energy. The difference in potential, electric potential energy is been turned into kinetic energy of the that free charge. So if q is positive and V2 is less than V1, we have to do work to move the charge. We're trying to move, push the charge in the opposite direction, to the direction that the electric field is trying to push its charge. So we have to add energy. So that picture, the charge starts off at a lower potential. And I have to push it up the hill. I have to add some energy to get that charge to a higher potential region. So, [COUGH] the other thing that's really key here, is that, all that matters is the difference in potential. It doesn't really matter what the absolute values of V2 and V1 are. All that matters is their difference. And so we can set the 0 anywhere we want. So instead of writing delta V all the time, we're just going to assume that there's some reference potential level that we're going to call 0. And then all voltages or all electric potentials are measure relative to that. And they're just expressed as V, the potential difference between wherever, whatever the potential is, say, in a circuit, and the reference potential. Which we'll see in a few minutes, is what we're going to define to be the ground of the circuit.