If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# Electric potential from multiple charges

## Video transcript

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 going to let a move but we do know the values of the charges we've got a positive one micro Coulomb charge a positive five micro Coulomb charge and a negative two micro Coulomb 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 going to be creating an electric potential at P we can just use the formula for the electric potential created by a charge 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 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 1 micro Coulomb charge is going to 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 1 micro Coulomb charge it's going to equal K which is always 9 times 10 to the 9th times the charge creating the electric potential which in this case is positive 1 microcoulombs micro means 10 to the negative sixth and the distance between this charge and the point we're considering to find the electric potential is going to be 4 meters so from here to there we're shown is 4 meters and we get a value of two thousand two hundred and fifty joules per Coulomb is the unit for electric potential but this is just the electric potential created at Point P by this positive 1 micro Coulomb charge all the rest of these charges are also going to create electric potential at Point P so if we want the total electric potential we're going to have to find the contribution from all these other charges at Point P as well so the electric potential from the positive 5 micro Coulomb charge is going to also be 9 times ix but this time times the charge creating it would be the five microcoulombs and again micro is ten to the negative sixth and now you've got to be careful I'm not going to 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 going to be this distance right here what is that going to be well if you imagine this triangle you've 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 4 squared take a square root which is just the Pythagorean theorem and that's going to be 9 plus 16 is 25 and the square root of 25 is just 5 so this is 5 meters from this charge to this point P so we'll plug in 5 meters here and if we plug this into the calculator we get 9 thousand joules per Coulomb so we've got one more charge to go this negative 2 microcoulombs is also going to create its own electric potential of point P so the electric potential created by the negative 2 micro Coulomb charge will again be 9 times 10 to the 9th this time times negative 2 microcoulombs again it's micro so 10 to the negative sixth 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 got to remember to include the negative the good news is these aren't vectors notice these are not going to 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 going to 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 are just going to 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 3 meters which if we solve gives us negative 6 thousand 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 two thousand two hundred and fifty joules per Coulomb plus nine thousand joules per Coulomb plus negative six thousand joules per Coulomb and we could put a parenthesis around this so it doesn't look so awkward so if you take 2250 plus nine thousand minus six thousand you get positive five thousand two hundred and fifty 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