Voltage

Before we move on, I want to
clarify something that I've

inadvertently done.

I think I was not exact
with some of the

terminology I used.

So I want to highlight the
difference between two things

that I've used almost
interchangeably up to this

point, but now that we are about
to embark on learning

what voltage is, I think it's
important that I highlight the

difference, because initially,
this can be very confusing.

I remember when I first learned
this, I found I often

mixed up these words and didn't
quite understand why

there was a difference.

So the two words are
electrical-- or sometimes

you'll see electric instead
of electrical.

So "electric potential energy"
and "electric potential." I

think even in the last video,
I used these almost

interchangeably, and I shouldn't
have. I really

should have always used
electrical or electric

potential energy.

And what's the difference?

Electrical potential energy is
associated with a charge.

It's associated with a particle
that has some charge.

Only that particle
can have energy.

Electrical potential, or
electric potential, this is

associated with a position.

So, for example, if I have a
charge and I know that it's at

some point with a given electric
potential, I can

figure out the electric
potential energy at that point

by just multiplying actually
this value by the charge.

Let me give you some examples.

Let's say that I have
an infinite

uniformly charged plate.

So that we don't have to do
calculus, we can have a

uniform electric field.

Let's say that this
is the plate.

I'll make it vertical just so we
get a little bit of change

of pace, and let's say it's
positively charged plate.

And let's say that the
electric field

is constant, right?

It's constant.

No matter what point we pick,
these field vectors should all

be the same length because the
electric field does not change

in magnitude it's pushing out,
because we assume when we draw

field lines that we're using a
test charge with a positive

charge so it's pushing
outward.

Let's say I have a
1-coulomb charge.

Actually, let me make
it 2 coulombs just

to hit a point home.

Say I have a 2-coulomb charge
right here, and it's positive.

A positive 2-coulomb charge, and
it starts off at 3 meters

away, and I want to bring
it in 2 meters.

I want to bring it in 2 meters,
so it's 1 meter away.

So what is the electric-- or
electrical-- potential energy

difference between the particle
at this point and at

this point?

Well, the electrical potential
energy difference is the

amount of work, as we've learned
in the previous two

videos, we need to apply to this
particle to take it from

here to here.

So how much work do
we have to apply?

We have to apply a force that
directly-- that exactly-- we

assume that maybe this is
already moving with a constant

velocity, or maybe we have to
start with a slightly higher

force just to get it moving, but
we have to apply a force

that's exactly opposite the
force provided by Coulomb's

Law, the electrostatic force.

And so what is that force we're
going to have to apply?

Well, we actually have to know
what the electric field is,

which I have not told you yet.

I just realized that,
as you can tell.

So let's say all of these
electric field lines are 3

newtons per coulomb.

So at any point, what is the
force being exerted from this

field onto this particle?

Well, the electrostatic force
on this particle is equal to

the electric field times the
charge, which is equal to-- I

just defined the electric field
as being 3 newtons per

coulomb times 2 coulombs.

It equals 6 newtons.

So at any point, the electric
field is pushing this way 6

newtons, so in order to push the
particle this way, I have

to completely offset that, and
actually, I have to get it

moving initially, and I'll
keep saying that.

I just want to hit
that point home.

So I have to apply a force of
6 newtons in the leftward

direction and I have to apply
it for 2 meters to get the

point here.

So the total work is equal to
6 newtons times 2 meters,

which is equal to 12
newton-meters or 12 joules.

So we could say that the
electrical potential energy--

and energy is always joules.

The electrical potential energy
difference between this

point and this point
is 12 joules.

Or another way to say it
is-- and which one

has a higher potential?

Well, this one does, right?

Because at this point, we're
closer to the thing that's

trying to repel it, so if we
were to just let go, it would

start accelerating in this
direction, and a lot of that

energy would be converted to
kinetic energy by the time we

get to this point, right?

So we could also say that the
electric potential energy at

this point right here is 12
joules higher than the

electric potential energy
at this point.

Now that's potential energy.

What is electric potential?

Well, electric potential tells
us essentially how much work

is necessary per unit
of charge, right?

Electric potential energy was
just how much total work is

needed to move it from
here to here.

Electric potential says, per
unit charge, how much work

does it take to move any charge
per unit charge from

here to here?

Well, in our example we just
did, the total work to move it

from here to here
was 12 joules.

But how much work did it take to
move it from there to there

per charge?

Well, work per charge is equal
to 12 joules for what?

What was the charge
that we moved?

Well, it was 2 coulombs.

It equals 6 joules
per coulomb.

That is the electric potential
difference between this point

and this point.

So what is the distinction?

Electric potential energy was
associated with a particle.

How much more energy did the
particle have here than here?

When we say electric potential,
because we

essentially divide by the
size of the particle, it

essentially is independent of
the size of the particle.

It actually just depends
on our position.

So electric potential, we're
just saying how much more

potential, irrespective of the
charge we're using, does this

position have relative
to this position?

And this electric potential,
that's just another way of

saying voltage, and the unit
for voltage is volts.

So 6 joules per coulomb,
that's the

same thing as 6 volts.

And so if we think of the
analogy to gravitation, we

said gravitational potential
energy was mgh, right?

This was force.

This was distance, right?

Electric potential is
essentially the amount of

gravitational-- if we extend
the analogy, the amount of

gravitational potential energy
per mass, right?

So if we wanted a quick way of
knowing what the gravitational

potential is at any point
without having to care about

the mass, we divide by the
mass, and it would be the

acceleration of gravity
times height.

Ignore that if it
confused you.

So what is useful
about voltage?

It tells us regardless of how
small or big or actually

positive or negative a charge
is, what the difference in

potential energy would be if
we're at two different points.

So electric potential, we're
comparing points in space.

Electric potential energy, we're
comparing charges at

points in space.

Hopefully, I didn't
confuse you.

In the next video, we'll
actually do a couple of

problems where we figure out
the electric potential

difference or the voltage
difference between two points

in space as opposed
to a charge at two

different points in space.

I will see you in
the next video.