- [Instructor] So imagine you had three charges
sitting next to each other, but they're fixed in place.
So somehow these charges are bolted down
or secured in place, we're not gonna let'em move.
But we do know the values of the charges.
We've got a positive one microcoulomb charge,
a positive five microcoulomb charge,
and a negative two microcoulomb charge.
So a question that's often asked when you have this type
of scenario is if we know the distances between the charges,
what's the total electric potential at some point,
and let's choose this corner,
this empty corner up here, this point P.
So we want to know what's the electric potential at point P.
Since we know where every charge is that's gonna be
creating an electric potential at P,
we can just use the formula for the electric potential
created by a charge and that formula is V equals k,
the electric constant times Q,
the charge creating the electric potential divided by r
which is the distance from the charge to the point
where it's creating the electric potential.
So notice we've got three charges here,
all creating electric potential at point P.
So what we're really finding is the
total electric potential at point P.
And to do that, we can just find the electric potential
that each charge creates at point P, and then add them up.
So in other words, this positive one microcoulomb charge
is gonna create an electric potential value at point P,
and we can use this formula to find what that value is.
So we get the electric potential from the
positive one microcoulomb charge, it's gonna equal k,
which is always nine times 10 to the ninth,
times the charge creating the electric potential
which in this case is positive one microcoulombs.
Micro means 10 to the negative six and the distance
between this charge and the point we're considering
to find the electric potential is gonna be four meters.
So from here to there, we're shown is four meters.
And we get a value 2250 joules per coulomb,
is the unit for electric potential.
But this is just the electric potential created at point P
by this positive one microcoulomb charge.
All the rest of these charges are also gonna create
electric potential at point P.
So if we want the total electric potential,
we're gonna have to find the contribution
from all these other charges at point P as well.
So the electric potential from the
positive five microcoulomb charge is gonna also be
nine times 10 to the ninth, but this time,
times the charge creating it would be
the five microcoulombs and again,
micro is 10 to the negative six,
and now you gotta be careful.
I'm not gonna use three meters or four meters
for the distance in this formula.
I've got to use distance from the charge
to the point where it's creating the electric potential.
And that's gonna be this distance right here.
What is that gonna be?
Well if you imagine this triangle,
you got a four on this side,
you'd have a three on this side,
since this side is three.
To find the length of this side, you can just do
three squared plus four squared, take a square root,
which is just the Pythagorean Theorem,
and that's gonna be nine plus 16, is 25
and the square root of 25 is just five.
So this is five meters from this charge to this point P.
So we'll plug in five meters here.
And if we plug this into the calculator,
we get 9000 joules per coulomb.
So we've got one more charge to go,
this negative two microcoulombs is also gonna create
its own electric potential at point P.
So the electric potential created by
the negative two microcoulomb charge
will again be nine times 10 to the ninth.
This time, times negative two microcoulombs.
Again, it's micro, so 10 to the negative six,
but notice we are plugging in the negative sign.
Negative charges create negative electric potentials
at points in space around them, just like positive charges
create positive electric potential values
at points in space around them.
So you've got to include this negative, that's the bad news.
You've gotta remember to include the negative.
The good news is, these aren't vectors.
Notice these are not gonna be
vector quantities of electric potential.
Electric potential is not a vector quantity.
It's a scaler, so there's no direction.
So I'm not gonna have to break this into components
or worry about anything like that up here.
These are all just numbers at this point in space.
And to find the total, we're just gonna add all these up
to get the total electric potential.
But they won't add up right if you don't include
this negative sign because the negative charges
do create negative electric potentials.
So what distance do we divide by is the distance between
this charge and that point P, which we're shown over here
is three meters, which if we solve, gives us
negative 6000 joules per coulomb.
So now we've got everything we need
to find the total electric potential.
Again, these are not vectors, so you can just literally
add them all up to get the total electric potential.
In other words, the total electric potential at point P
will just be the values of all of the potentials
created by each charge added up.
So we'll have 2250 joules per coulomb
plus 9000 joules per coulomb
plus negative 6000 joules per coulomb.
And we could put a parenthesis around this
so it doesn't look so awkward.
So if you take 2250 plus 9000 minus 6000,
you get positive 5250 joules per coulomb.
So that's our answer.
Recapping to find the total electric potential
at some point in space created by charges,
you can use this formula to find the electric potential
created by each charge at that point in space
and then add all the electric potential values you found
together to get the total electric potential
at that point in space.