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# Voltage

Sal explains the difference between electrical potential (voltage) and electrical potential energy. Created by Sal Khan.

Video transcript

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.