Two charges q₁ and q₂ are placed at (0, 0, d) and (0, 0, –d) respectively. Find locus of points where the potential a zero.

Given

Positon of charge with magnitude q₁ = (0, 0, d)

Positon of charge with magnitude q₂ = (0, 0, -d)

The potential due to a point charge q at a distance r is given by

Let the potential of due to the two charges at any point having coordinates (x, y, z) be V, then

Where

and

Therefore, the equation for potential becomes:

If the potential is zero then, V=0

Squaring both sides, we have

Using the property

We have,

Comparing the equation with the general equation of a sphere, we have

The center of the sphere to be a=0, b=0 and c=, therefore the equipotential surface is a sphere with center [0, 0,