the concept of what we call electric field.

We spend the whole lecture on electric fields.

If I have a -- a charge, I just choose Q,

capital Q and plus at a particular location and at

another location I have another charge little Q,

I think of that as my test charge.

And there is a separation between the two which is R.

The unit vector from capital Q to li- little Q is this vector.

And so now I know that the two charges if they were positive --

let's suppose that little Q is positive, they would repel each

other. Little Q is negative they would

attract each other. And let this force be F and

last time we introduced Coulomb's law that force equals

little Q times capital Q times Coulomb's constant divided by R

squared in the direction of R roof.

The two have the same sign. It's in this direction.

If they have opposite sign it's in the other direction.

And now I introduce the idea of electric field for which we

write the symbol capital E.

And capital E at that location P where I have my test charge

little Q at that location P is simply the force that a test

charge experienced divided by that test charge.

So I eliminate the test charge. So I get something that looks

quite similar but it doesn't have the little Q in it anymore.

And it is also a vector. And by convention,

we choose the force such that if this is a positive test

charge then we say the E field is away from Q if Q is positive,

if Q is negative the force is in the other direction,

and therefore E is in the other direction.

So we adopt the convention that the E field is always in the

direction that the force is on a positive test charge.

What you have gained now is that you

have taken out the little Q. In other words the force here

depends on little Q. Electric field does not.

The electric field is a representation for what happens

around the charge plus Q. This could be a very

complicated charge configuration.

An electric field tells you something about that charge

configuration. The unit for electric field you

can see is newtons divided by coulombs.

In SI units and normally we won't even indicate the um the

unit, we just leave that as it is.

Now we have graphical representations for the electric

field. Electric field is a vector.

So you expect arrows and I have here an example of a -- a charge

plus three. So by convention the arrows are

pointing away from the charge in the same direction that a

positive test charge would experience the

force. And you notice that very close

to the charge the arrows are larger than farther away.

That it that sort of represents is trying to represent the

inverse R square relationship. Of course it cannot be very

quantitative. But the basic idea is this is

of course spherically symmetric, if this is a point charge.

The basic idea is here you see the field vectors and the

direction of the arrow tells you in which direction the force

would be. If it is a positive test

charge. And the length of the vector

give you an idea of the magnitude.

And here I have another charge minus one.

Doesn't matter whether it is minus one coulomb or minus

microcoulomb. Just it's a relative

representation. And you see now that the E

field vectors are reversed in direction.

They're pointing towards the minus charge by convention.

And when you go further out they are smaller and you have to

go all the way to infinity of course

for the field to become zero. Because the one over R square

field falls off and you have to be infinitely far away for you

to not experience at least in principle any effect from the

from the charge. What do we do now when we have

more than one charge? Well, if we have several

charges -- here we have Q one and here we have Q two and here

we have Q three and let's say here we

have Q of I, we have I charges.

And now we want to know what is the electric field at point P.

So it's independent of the test charge that I put here.

You can think of it if you want to as the the force per unit

charge. You've divided out the charge.

So now I can say what is the E field due to Q one alone?

Well, that would be if Q one were

positive then this might be a representation for E one.

If Q two were negative, this might be a representation

for E two, pointing towards the negative charge.

And if this one were negative, then I would have here a

contribution E three, and so on.

And now we use the superposition principle as we

did last time with Coulomb's law, that the

net electric field at point P as a vector is E one in

reference of charge Q one plus the vector E two plus E three

and so on and if you have I charges it is the sum of all I

charges of the individual E vectors.

Is it obvious that the superposition principle works?

No. Does it work?

Yes. How do we

know it works? Because it's consistent with

all our experimental results. So we take the superposition

principle for granted and that is acceptable.

But it's not obvious. If you tell me what the

electric field at this point is which is the vectorial sum of

the individual E field vectors then I can always tell you what

the force will be if I bring a charge at that location.

I take any charge that I always would carry in my pocket,

I take it out of my pocket and I put it at that location.

And the charge that I have in my pocket is little Q.

Then the force on that charge is always Q times E.

Doesn't matter whether Q is positive.

Then it will be in the same direction as E.

If it is negative it will be in the opposite direction as E.

If Q is large the force will be large.

If Q is small the force will be small.

So once you know the E field it could be the result of

very complicated charge configurations,

the real secret behind the concept of an E field is that

you bring any charge at that location and you know what force

acts at that point on that charge.

If we try to be a little bit more quantitative,

suppose I had here a charge plus three and here I had a

charge minus one. Here's minus one.

And I want to know what the field configuration is as a

result of these two charges. So you can go to any particular

point. You get an E vector which is

going away from the plus three, you get one that goes to minus

one, and you have to vectorially add the two.

If you are very close to minus one, it's very clear because of

the inverse R square relationship that the minus one

is probably going to win.

Let's in our mind take a plus test charge now.

And we put a plus test charge very close to minus one,

say put it here, even though plus three is

trying to push it out, clearly minus one is most

likely to win. And so there will probably be a

force on my test charge in this direction.

The net result of the effects of the two.

Suppose I take the same positive test charge and I put

it here, very far away, much farther away than this

separation. What do you think now is the

direction of the force on my plus charge?

Very far away. Excuse me.

Why do you think it's to the left?

Do you think minus one wins? A: [inaudible].

Do you really think the minus one is stronger than the plus

three because the plus three will push it out and

the minus one tries to lure it in, right, if the test charge is

positive. A:

plus two. So if you're far away from a

configuration like this, even if you were here,

or if you were there, or if you're way there,

clearly the field is like a plus two charge.

And falls off as one over R squared.

So therefore if you're far away the force is in this direction.

And now look, what is very interesting.

Here if you're close to the minus one, the force is in this

direction. Here when you're very far away,

maybe I should be all the way here, it's in that direction.

So that means there must be somewhere here

the point where the E field is zero.

Because if the force is here in this direction but ultimately

turns over in that direction, there must be somewhere a point

where E is zero. And that is part of your

assignment. I want you to find that point

for a particular charge configuration.

So let's now go to some graphical representations of a

situation which is actually plus three minus one,

try to improve on the light situation.

And let's see how these electric vectors,

how they show up in the vicinity of these two charges.

So here you see the plus three and the minus one,

relative units, and let's take a look at this

in some detail. First of all the length of the

arrows again indicates the strength.

It gives you a feeling for the strength.

It's not very quantitative of course.

And so let's first look at the plus three, which is very

powerful. You see that these arrows all

go away from the plus three and when you're closer to the plus

three, they're stronger, which is a representation of

the inverse R square field. If you're very close to the

minus one, ah the arrows are pointing in towards the minus

one, because the one over R square, the minus one wins.

And so you see they're clearly going into the

direction of the minus one. Well, if you're in between the

plus and the minus on this line, always the E field will be

pointing from the plus to the minus.

Because the plus is pushing out and the minus is sucking in.

So the two support each other. But now if you go very far away

from this charge configuration, anywhere but very far away,

much farther than the distance between the two charges,

so somewhere here, or somewhere there,

or somewhere there, or here, notice that always the

arrows are pointing away. And the reason is that plus

three and minus one is as good as a plus two if you're very

very far away. But of course when you're very

close in, then the field configuration can be very very

complicated. But you see very clearly that

these arrows are all pointing outwards.

None of them come back to the minus one.

None of them point to the minus one direction.

And that's because the plus three is more powerful and then

there is here this point and only point

whereby the electric field is zero, if you put a positive test

charge here, the minus will attract it, the plus will repel

it, and therefore there comes a point where the two cancel each

other exactly. Now there is another way of

electric field representation which is more organized.

And we call these field lines. So you see again the plus three

and you see there the minus one.

If I release right here or I place here a positive test

charge all I know is that the force will be tangential to the

field lines. That is the meaning of these

lines. So if I'm here the force will

be in this direction. If I put a positive test charge

here, the force will be in this direction, and of course,

if it's a negative charge the force flips over.

So the meaning of the field lines are that it always tells

you in which direction a charge experiences a force.

A force a positive charge always in the direction of the

arrows, tangentially to the field lines and a negative

charge in the opposite direction.

How many field lines are there in space?

Well of course there are an infinite number.

Just like these little arrows that we had before,

we only sprinkled in a few but of

course in every single point there is an electric field and