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.