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### Course: AP®︎/College Physics 2 > Unit 2

Lesson 3: Electric potential energy, electric potential, and voltage- Electric potential at a point in space
- Electric potential from multiple charges
- Electric potential: definition
- Electric potential: conceptual problems (part 1)
- Electric potential energy of charges
- Potential energy of a system of 3 charges
- Potential energy of a system of charges: Numerical
- Potential energy of a system of charges (intermediate)
- System of charges in an electric field

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# Electric potential from multiple charges

In this video David shows how to find the total electric potential at a point in space due to multiple charges. Created by David SantoPietro.

## Want to join the conversation?

- David says that potential is scalar, because PE is scalar -- but vectors must come into play when we place a charge at point "P" and release it?

The calculation for potential at point "P" is +5,250 J/C, so if we place a +1 C charge there, then it will have 5,250 J of PE. Once we place that +1 C charge there and release it, the 5,250 J of PE will convert into KE and the charge will move -- but it will move in a specific, predictable path -- won't it?

How can we determine the path that any charge would take upon being placed in that position?(32 votes) - Can the potential at point P be determined by finding the work done in bringing each charge to that point?(4 votes)
- just one charge is enough. one unit charge brought from infinity.

then the potential is the work done, (per unit charge) in bringing it from infinity to that point

ok?(5 votes)

- So if we're trying to calculate a scalar quantity, we plug in signs based on charge. If we're trying to calculate a vector quantity, we plug in signs based on direction. Correct?(3 votes)
- About this whole exercise, we calculated the total electric potential at a point in space (p) relative to which other point in space?

And the final result tells us that a charge of 1 Coulomb on the point p can do 5250J of work ("displacement against a force") more than any other point?

Thanks!(2 votes)- the potential at infinity is defined as being zero.

The potential at a point is the amount of work it will do (or will be done to it) in moving it to infinity. Depending on the sign of charge(3 votes)

- In this video, are the values of the electric potential due to all the three charges absolute potential (i.e. with respect to infinity)?(1 vote)
- there is no such thing as absolute potential but when you use the equation kQQ/r you are implicitly setting zero at infinity.(4 votes)

- 2. Two point charges each of magnitude q are fixed at the points (0, +a) and

(0, –a) in the Cartesian coordinate system.

i. Draw a diagram showing the positions of the charges.

ii. What is the potential Vo at the origin?

iii. Show that the potential at any point on the x-axis the potential is

given by

2 2 2 2

0

0

1 2

4 2

q q V

a x a x

iv. At what values of x is the potential one half of that at the origin?

v. Sketch the variation of the potential along the x-axis as a function

of x.(2 votes) - If i have a charged spherical conductor in side another bigger spherical shell and i made a contact between them what will happen ?

does they balance at equal electric potential ?

or the charge goes to the outer shell ?

and why?(1 vote) - Why is the electric potential a scalar? Which way would a particle move?(1 vote)
- Electric potential is just a value without a direction. The direction of the changed particle is based the differences in the potential not from the magnitude of the potential. This change in potential magnitude is called the gradient.(1 vote)

- 1. If the distance given in a problem is in cm (rather than m), how does that effect the "j/c" unit (if at all)?

2. If I wanted to calculate how much energy it takes to move one of these charges from its current place to a place a few meters over, could I just say that movement would take the EP measurement of one point (ex: 2,250J/C for V1) times the amount of Coulumbs the point has? AKA: How would I calculate the amount of energy needed to move a point?(1 vote) - Wouldn't you have to do trig to break down the +5C charge since it would have an X and a Y component, meaning it can't be added to either the +1 charge, and the -2 charge, both of which being an X and a Y respectively?(1 vote)
- Firstly, potential is a scalar, not a vector, so V_tot = V1+V2+V3+...

Secondly, potential isn't to be confused with field. Also, when dealing with field (which is a vector), we don't break up the charge, we break up the**field**into components.(1 vote)

## Video transcript

- [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 scalar, 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.