All language subtitles for LS4U2B1

We've talked now about potential,
the idea of potential.

Let's actually calculate it.

Let's calculate the potential
near a point charge.

And just to save me a lot of time and
a lot of chalk and a lot of breath,

from now on, the rest of the class,
when I say potential, I mean the

electric potential.

I'm not going to say electric
every time anymore.

If I mean energy, I'll
say potential energy.

But if I just mean electric potential,
I'm just going to call it potential.

So there it is.

Just the potential, OK?

So we're going to start with
a point charge, or we might

say a sphere of charge.

We can call it a sphere of charge plus
q, and have field lines coming out

like this, like that, and more field
lines that I like to draw like that.

And let's think about the potential of
a charge as it moves from point A to

point B.

So we're going from A to B. And first,
we want to calculate the change in

potential energy.

We'll get to the potential in a minute,
but first the change in

potential energy.

So potential energy we usually
label as delta u.

And you have to be very specific
about the two points.

So we're going to talk about delta u if
we took a little test charge, plus

q, from A to B.

And even that is difficult when
you think about energy.

And one way to prove that is when I
teach this class, and I have 300 of

these brilliant little Rice freshman
minds in here, I ask them the

following very simple question.

I walk into a coffee shop with $10.

And I walk out with a cup
of coffee and $8.

What's the difference in my money?

So here you just shout out.

What is the difference in my money?

Walk in with 10, walk out with 8.

And I bet you if you're like all
these brilliant Rice minds

here, you said $2.

And that's wrong.

You lost $2.

The difference in your money
is negative $2 if

we're going to be technical.

So in the mathematical world, difference
is always the final minus

the initial.

Always.

So if my final was $8, and my initial
was $10, it's minus $2.

So you've got to be careful with
negative signs when you do changes in

energy and changes in potential.

Now, when we speak in language, we often
have words that account for the

negative sign.

I went to the coffee
shop and I lost $2.

Well, the "lost" implies
the negative sign.

I "blew" $2, et cetera. "Blew"
means you exploded the $2.

So all these numbers, all these words
can give you the negative sign.

But in physics, we can't
just use a word.

We have to actually make
sure we have it right.

So a difference is always
final minus initial.

Let's see.

So what is that energy going to
be if we go from here to here?

If we just have the test charge here and
just let it go, it's going to feel

a force pushing it that way.

It's going to naturally just
fly from here to here.

So in this sort of work and energy
stuff, you've got to

think about the system.

There's external and
internal, all that.

I'm not going to review
that in great detail.

But here, the system is the charge,
and the big charge, and the little

test charge, and the
fields they create.

So the system is doing the work.

As the charge flies from here to here,
the force is due to the system.

So this is what's called
internal work.

The system does the work.

When the system does the
work, it's negative.

The change in potential is
negative work internal.

Because if the system does this work,
it's giving up some of its potential

energy to do the work.

That's why the change in
potential is negative.

It's losing some energy for
the work that it does.

So that one is negative w int.

So we calculate this work,
and what is it?

Well, we bring the negative along,
and work is the integral from A

to B of F dot ds.

You [? can about ?] think of
work as just F times x.

But when you're really doing integrals
and things are changing, its integral

of F dot ds.

So there's no inherent negative
sign on this integral.

Work is this integral, and I'm
carrying the negative along.

So then we just have to say,
well, what's the force?

The force is just the charge,
q, times the big field e.

So we write it one more time.

It's equal to the negative integral
from A to B of the test

charge q E dot ds.

And remember, the little ds's are the
little steps we're taking as we go

from A to B. There's you're little ds.

So you can look at this and decide
if this looks right.

So we aren't doing potential yet.

We're still on energy.

But we're saying that the energy
should come out what?

It should come out negative.

We're losing energy.

We're going from here.

We're gaining a lot of kinetic,
so we must be losing energy.

So this thing should
come out negative.

It's got a negative sign there.

That's a good sign.

Will the integral come out positive?

Yes.

The charge is positive.

The E field has a positive magnitude,
and so does the ds.

And they're in the same direction.

E and ds are together.

So this integral is going
to come out positive.

There's a negative sign there.

Therefore, the change in
energy is negative.

Everything's fine.