Electrons and insulators are bound to the atoms and to the

molecules, unlike conductors, where they can freely move,

and when I apply an external field -- for instance,

a field in this direction, then even though the molecules

or the atoms may be completely spherical, they will become a

little bit elongated in the sense that the electrons will

spend a little bit more time there than they used to,

and so this part become negatively charged and this part

becomes positively charged, and that creates a dipole.

I discussed that with you, already, during the first

lecture, because there's something quite remarkable about

this, that if you have an insulator -- notice the pluses

and the minuses indicate neutral atoms -- and if now,

I apply an electric field, which comes down from the top,

then, you see a slight shift of the electrons,

they spend a little bit more time up than down,

and what you see now is, you see a layer of negative

charge being created at the top,

and a layer of positive charge being created at the bottom.

That's the result of induction, we call that also,

sometimes, polarization. You are polarizing,

in a way, the electric charge. Uh, substances that do this,

we call them dielectrics, and today, we will talk quite a

bit about dielectrics. The first part of my lecture is

on the web, uh, if you go eight oh two web,

you will see there a document which

describes, in great detail, what I'm going to tell you

right now. Suppose we have a plane

capacitor -- two -- planes which I charge with certain potential,

and I have on here, say, a charge plus sigma and

here I have a charge minus sigma.

I'm going to call this free -- you will see,

very shortly why I call this free -- and this is minus free.

So there's a potential difference between the plate,

charge flows on there, it has an area A,

and sigma free is the charge density, how much charge per

unit area. So we're going to get an

electric field, which runs in this direction,

and I call that E free. And the distance between the

plates, say, is D. So this is a given.

I now remove the power supply that I used to give it a certain

potential difference. I completely take it away.

So that means that this charge here is trapped,

can not change. But now I move in a dielectric.

I move in one of those substances.

And what you're going to see here, now, at the top,

you're going to see a negative-induced layer,

and at the bottom, you're going to see a

positive-induced layer. I called it plus-sigma-induced,

and I call this minus-sigma-induced.

And the only reason why I call the

other free, is to distinguish them from the induced charge.

This induced charge, which I have in green,

will produce an electric field which is in the opposite I-

direction, and I call that E-induced.

And clearly, E free is, of course,

the surface charge density divided by epsilon zero,

and E-induced is the induced surface charge density,

divided by epsilon zero.

And so the net E field is the vectorial sum of the two,

so E net -- I gave it a vector -- is E free plus E induced,

vectorially added. Since I'm interested -- I know

the direction already -- since I'm interested in magnitudes,

therefore the strength of the net E field is going to be the

strengths of the E fields created by the so-called free

charge, minus the strengths of the E fields created by the

induced charge, minus -- because this E vector

is down, and this one is in the up direction.

And so, if I now make the assumption that a certain

fraction of the free charge is induced, so I make the

assumption that sigma-induced is some fraction B times sigma

free, I just write,

now, and I for induced and an F for free.

B is smaller than one. If B were point one,

it means that sigma-induced would be ten percent of sigma

free, that's the meaning of B. So clearly, if this is the

case, then, also, E of I must also me B times E

of F. You can tell immediately,

they are connected. And so now I can write down,

for E net, I can also write down E

free times one minus B, and that one minus B,

now, we call one over kappa. I call it one over kappa,

our book calls it one over K. But I'm so used to kappa that I

decided to still hold on to kappa.

And that K, or that kappa, whichever you want to call it,

is called the dielectric constant.

It's a dimensionless number. And so I can write down,

now, in general, that E -- and I drop the word

net, now, from now on, whenever I write E,

throughout this lecture, it's always the net electric

field, takes both into account. So you can write down,

now, that E equals the free electric fields,

divided by kappa, because one minus B is one over

kappa. And so you see,

in this experiment that I did in my head, first,

bringing charge on the plate, certain potential difference,

removing the power supply, shoving in the dielectric that

an E field will go down by a factor kappa.

Kappa, for glass, is about five.

That will be a major reduction, I will show you that later.

If the electric field goes down, in this particular

experiment, it is clear that the potential difference between the

plates will also go down, because the potential

difference between the plates V is always the electric field

between the plates times D. And so, if this one goes down,

by a factor of kappa, if I just shove in the

dielectric, not changing D, then, of course,

the potential between the plates is also going down.

None of this is so intuitive, but I will demonstrate that

later. The question now arises,

does Gauss' Law still hold? And the answer is,

yes, of course, Gauss' Law will still hold.

Gauss' Law tells me that the closed loop -- closed surface,

I should say, not closed loop -- the closed

surface integral of E dot D A is one over epsilon times the sum

of all the charges inside my box.

All the charges! The net charges,

that must take into account both the induced charge,

as well as the free charge.

And so let me write down here, net, to remind you that.

But Q net is, of course, Q free plus Q

induced. And I want to remind you that

this is minus, and this was plus.

The free charge, positive there,

is plus, and at that same plate, if you have your Gaussian

surface at the top, you have the negative charged Q

induced. And so therefore,

Gauss' Law simply means that you have to take both into

account, and so, therefore, you can write down

one over epsilon zero, times the sum of Q free,

but now you have to make sure that you take the induced charge

into account, and therefore,

you divide the whole thing by kappa.

Then you have automatically taken the induced charge into

account. So you can amend mex- uh,

Gauss' Law very easily by this factor of kappa.

Dielectric constant is dimensionless,

as I mentioned already, it is one, in vacuum,

by definition. One atmosphere gases typically

have dielectric constant just a hair larger than one.

We will, most of the time, assume that it is one.

Plastic has a dielectric constant of three,

and glass, which is an extremely good insulator,

has a dielectric constant of five.

If you have an external field, that can induce dipoles in

molecules -- but there are substances, however,

which themselves are already dipoles, even in the absence of

an electric field. If you apply,

now, an external field, these dipoles will start to

align along the electric field, we did an experiment once,

with some grass seeds, perhaps you remember that.

And as they align in the direction of the electric field,

they will strengthen the electric

field. On the other hand,

because of the temperature of the substance,

these dipoles, these molecules which are now

dipoles by themselves, through chaotic motion,

will try to disalign, temperature is trying to

disalign them. So it is going to be a

competition, on the one hand, between the electric field

which tries to align them and the temperature which tries to

disalign them. But if the electric field is

strong, you can get a substantial amount of alignment.

Uh, permanent dipoles, as a rule, are way stronger

that any dipole that you can induce by ordinary means in a

laboratory, and so the substances which are natural

dipoles, they have a much higher value for kappa,

a much higher dielectric constant that the substances

that I just discussed, which themselves,

do not have dipoles. Water is an example,

extremely good example. The electrons spend a little

bit more time near the oxygen than near

the hydrogen, and water has a dielectric

constant of eighty. That's enormous.

And if you go down to lower temperature, if you take ice of

minus forty degrees, it is even higher,

then the dielectric constant is one hundred.

I'm now going to massage you through four demonstrations,

four experiments. One of them,

you have already seen. And try to follow them as

closely as you can, because if you miss

one small step, then you miss,

perhaps, a lot. I have two parallel plates

which a- are on this table, as you have seen last time,

and I have, here, a current meter,

I put it -- an A on there, that means amp meter.

And the plates have a certain separation D.

I'm going to charge this capacitor up by connecting these

ends to a power supply, and I'm going to connect them

to fifteen hundred volts. I'm -- I'm already going to set

my light, because that's where you're going to see it very

shortly. I'm going to start off with a

distance D -- so this is going to be my experiment one -- with

a distance D of one millimeter. And the voltage V always means

the voltage the -- the -- the potential difference between the

plates is going to be fifteen hundred volts.

Forgive me for the two Vs, I can't help that.

This means, here, the potential difference,

and this is the unit in volts. Once I have charged them,

I disconnect -- this is very important -- I disconnect the

power supply, for which I write P S.

That's it. So the charge is now trapped.

As I charge it, as you saw last time,

you will see that the amp meter shows a short surge of current,

because, as I put charge on the plates, the charge has to go

from the power supply to the plates, and you will see a short

surge of current which will make the handle -- the hand of the

power su- of the amp meter, as you will see on the -- on

the wall there -- go to the right side, just briefly,

and then come back. This indicates that you are

charging the plates. Now, I'm going to open up the

gap -- so this is my initial condition, there is no

dielectric -- and now I'm going to go D to

seven millimeters. And this is what I did last

time. The reason why I do it again,

because I need this for my next demonstration.

If I make the distance seven millimeters, then the charge,

which I call now, Q free, but it is really the

charge on the plates, is not going to be -- is not

going to change, it is trapped.

So there can be no change when I open up the gap.

That means the amp meter will do

nothing, you will not see any charge flow.

The electric field E is unchanged, because E is sigma

divided by epsilon zero. If sig- if Q free is not

changing, sigma cannot change. So, no change in the electric

field. But the potential V is now

going to go up by a factor of seven, because V equals E times

D. E remains constant,

D goes up, V has to go up. And this is what I want to show

you first, even though you have already seen this.