# Potential of two point charges

## Homework Statement

Two point charges q1 and q2 are located on a straight line normal to a grounded (V=0) conducting plane. Choosing the z axis to go through the charges, q1 is at a distance z1 above the conductor, and q2 is at a distance z2.

Find the potential V(x,y,z) everywhere above the conductor.

## The Attempt at a Solution

I know the formula for the potential of 1 point charge in open space. I can also use image charges to define the potential at a point V(x,y,z > 0). But for two charges, would the potential at any point be the sum of the individual potentials?

## Answers and Replies

Spinnor
Gold Member
Yes, the potential at a point (x,y,z > 0) is the sum of the potentials due to the two real and two virtual charges. Otherwise how would you ever get the potential to be zero at z=0?

So as of now, my answer is

q1/(4pi e0) * 1/r [from (z-d) to (z+d)]

and in cartesian coordinates, r is (x^2 + y^2 + z^2)^1/2

and i would just sum this up with the same process except for q2?