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- [Instructor] So imagine
you had three charges

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sitting next to each other,
but they're fixed in place.

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So somehow these charges are bolted down

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or secured in place, we're
not gonna let'em move.

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But we do know the values of the charges.

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We've got a positive
one microcoulomb charge,

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a positive five microcoulomb charge,

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and a negative two microcoulomb charge.

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So a question that's often
asked when you have this type

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of scenario is if we know the
distances between the charges,

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what's the total electric
potential at some point,

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and let's choose this corner,

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this empty corner up here, this point P.

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So we want to know what's the
electric potential at point P.

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Since we know where every
charge is that's gonna be

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creating an electric potential at P,

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we can just use the formula
for the electric potential

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created by a charge and
that formula is V equals k,

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the electric constant times Q,

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the charge creating the
electric potential divided by r

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which is the distance from
the charge to the point

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where it's creating
the electric potential.

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So notice we've got three charges here,

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all creating electric
potential at point P.

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So what we're really finding is the

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total electric potential at point P.

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And to do that, we can just
find the electric potential

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that each charge creates at
point P, and then add them up.

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So in other words, this
positive one microcoulomb charge

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is gonna create an electric
potential value at point P,

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and we can use this formula
to find what that value is.

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So we get the electric potential from the

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positive one microcoulomb
charge, it's gonna equal k,

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which is always nine
times 10 to the ninth,

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times the charge creating
the electric potential

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which in this case is
positive one microcoulombs.

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Micro means 10 to the
negative six and the distance

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between this charge and
the point we're considering

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to find the electric potential
is gonna be four meters.

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So from here to there,
we're shown is four meters.

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And we get a value 2250
joules per coulomb,

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is the unit for electric potential.

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But this is just the electric
potential created at point P

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by this positive one microcoulomb charge.

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All the rest of these
charges are also gonna create

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electric potential at point P.

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So if we want the total
electric potential,

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we're gonna have to find the contribution

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from all these other
charges at point P as well.

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So the electric potential from the

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positive five microcoulomb
charge is gonna also be

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nine times 10 to the ninth, but this time,

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times the charge creating it would be

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the five microcoulombs and again,

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micro is 10 to the negative six,

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and now you gotta be careful.

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I'm not gonna use three
meters or four meters

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for the distance in this formula.

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I've got to use distance from the charge

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to the point where it's
creating the electric potential.

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And that's gonna be this
distance right here.

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What is that gonna be?

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Well if you imagine this triangle,

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you got a four on this side,

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you'd have a three on this side,

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since this side is three.

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To find the length of
this side, you can just do

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three squared plus four
squared, take a square root,

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which is just the Pythagorean Theorem,

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and that's gonna be nine plus 16, is 25

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and the square root of 25 is just five.

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So this is five meters from
this charge to this point P.

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So we'll plug in five meters here.

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And if we plug this into the calculator,

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we get 9000 joules per coulomb.

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So we've got one more charge to go,

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this negative two microcoulombs
is also gonna create

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its own electric potential at point P.

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So the electric potential created by

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the negative two microcoulomb charge

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will again be nine times 10 to the ninth.

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This time, times negative
two microcoulombs.

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Again, it's micro, so
10 to the negative six,

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but notice we are plugging
in the negative sign.

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Negative charges create
negative electric potentials

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at points in space around them,
just like positive charges

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create positive electric potential values

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at points in space around them.

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So you've got to include this
negative, that's the bad news.

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You've gotta remember
to include the negative.

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The good news is, these aren't vectors.

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Notice these are not gonna be

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vector quantities of electric potential.

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Electric potential is
not a vector quantity.

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It's a scaler, so there's no direction.

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So I'm not gonna have to
break this into components

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or worry about anything like that up here.

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These are all just numbers
at this point in space.

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And to find the total, we're
just gonna add all these up

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to get the total electric potential.

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But they won't add up
right if you don't include

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this negative sign because
the negative charges

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do create negative electric potentials.

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So what distance do we divide
by is the distance between

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this charge and that point P,
which we're shown over here

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is three meters, which
if we solve, gives us

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negative 6000 joules per coulomb.

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So now we've got everything we need

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to find the total electric potential.

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Again, these are not vectors,
so you can just literally

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add them all up to get the
total electric potential.

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In other words, the total
electric potential at point P

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will just be the values
of all of the potentials

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created by each charge added up.

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So we'll have 2250 joules per coulomb

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plus 9000 joules per coulomb

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plus negative 6000 joules per coulomb.

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And we could put a parenthesis around this

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so it doesn't look so awkward.

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So if you take 2250 plus 9000 minus 6000,

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you get positive 5250 joules per coulomb.

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So that's our answer.

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Recapping to find the
total electric potential

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at some point in space created by charges,

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you can use this formula to
find the electric potential

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created by each charge
at that point in space

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and then add all the electric
potential values you found

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together to get the
total electric potential

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at that point in space.