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

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inadvertently done.

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I think I was not exact
with some of the

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terminology I used.

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So I want to highlight the
difference between two things

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that I've used almost
interchangeably up to this

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

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

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difference, because initially,
this can be very confusing.

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

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mixed up these words and didn't
quite understand why

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there was a difference.

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So the two words are
electrical-- or sometimes

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you'll see electric instead
of electrical.

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

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think even in the last video,
I used these almost

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interchangeably, and I shouldn't
have. I really

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should have always used
electrical or electric

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potential energy.

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And what's the difference?

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Electrical potential energy is
associated with a charge.

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

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Only that particle
can have energy.

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Electrical potential, or
electric potential, this is

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associated with a position.

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

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some point with a given electric
potential, I can

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figure out the electric
potential energy at that point

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by just multiplying actually
this value by the charge.

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Let me give you some examples.

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Let's say that I have
an infinite

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uniformly charged plate.

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

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uniform electric field.

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Let's say that this
is the plate.

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

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

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And let's say that the
electric field

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is constant, right?

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It's constant.

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

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be the same length because the
electric field does not change

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

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

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charge so it's pushing
outward.

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

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Actually, let me make
it 2 coulombs just

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to hit a point home.

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

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

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

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

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

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difference between the particle
at this point and at

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this point?

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Well, the electrical potential
energy difference is the

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

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

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here to here.

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So how much work do
we have to apply?

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

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assume that maybe this is
already moving with a constant

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

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

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

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Law, the electrostatic force.

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

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

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which I have not told you yet.

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I just realized that,
as you can tell.

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

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newtons per coulomb.

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

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field onto this particle?

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Well, the electrostatic force
on this particle is equal to

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

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just defined the electric field
as being 3 newtons per

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coulomb times 2 coulombs.

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It equals 6 newtons.

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

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

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

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moving initially, and I'll
keep saying that.

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I just want to hit
that point home.

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

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

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point here.

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

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

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So we could say that the
electrical potential energy--

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and energy is always joules.

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The electrical potential energy
difference between this

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point and this point
is 12 joules.

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

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has a higher potential?

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Well, this one does, right?

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

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

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start accelerating in this
direction, and a lot of that

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energy would be converted to
kinetic energy by the time we

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get to this point, right?

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So we could also say that the
electric potential energy at

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this point right here is 12
joules higher than the

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electric potential energy
at this point.

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Now that's potential energy.

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What is electric potential?

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Well, electric potential tells
us essentially how much work

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is necessary per unit
of charge, right?

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Electric potential energy was
just how much total work is

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needed to move it from
here to here.

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Electric potential says, per
unit charge, how much work

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does it take to move any charge
per unit charge from

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here to here?

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

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from here to here
was 12 joules.

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

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per charge?

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

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What was the charge
that we moved?

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Well, it was 2 coulombs.

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It equals 6 joules
per coulomb.

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That is the electric potential
difference between this point

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and this point.

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So what is the distinction?

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Electric potential energy was
associated with a particle.

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

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When we say electric potential,
because we

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essentially divide by the
size of the particle, it

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essentially is independent of
the size of the particle.

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It actually just depends
on our position.

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

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

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position have relative
to this position?

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

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saying voltage, and the unit
for voltage is volts.

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So 6 joules per coulomb,
that's the

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same thing as 6 volts.

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

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said gravitational potential
energy was mgh, right?

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This was force.

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This was distance, right?

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Electric potential is
essentially the amount of

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

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gravitational potential energy
per mass, right?

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

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potential is at any point
without having to care about

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

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acceleration of gravity
times height.

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Ignore that if it
confused you.

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So what is useful
about voltage?

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It tells us regardless of how
small or big or actually

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positive or negative a charge
is, what the difference in

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

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

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Electric potential energy, we're
comparing charges at

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points in space.

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Hopefully, I didn't
confuse you.

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

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problems where we figure out
the electric potential

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difference or the voltage
difference between two points

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in space as opposed
to a charge at two

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different points in space.

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I will see you in
the next video.

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