Question

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

Answer 1

We assume that charges q1 and q2 are of opposite signs ie: one positive (+) and other negative (-), failing which there will be no region of zero potential.

Potential due to q1 (V1) = Kq1 / d1
Potential due to q2 (V2) = Kq2 / d2

Since they are of opposite signs, V1 + V2 = 0
Kq1 / d1 = Kq2 / d2
If both are of same magnitude, we get that d1 = d2
This mean that all points along Y axis will have potential zero