Two point charges of magnitude +q and -q are placed at (-d/2, 0,0) and (d/2, 0,0), respectively. Find the equation of the equipotential surface where the potential is zero.

Question

Philoid · Accepted Answer

Given

Magnitude of charge at position (-d/2, 0,0) = q

Magnitude of charge at position (d/2, 0,0) =- q

An equipotential surface is a surface on which all points have the same electric potential. The potential due to a point charge q at a distance r is given by

Thus for the system of charges given, the electric potential at any point P, is given by

Let the coordinates of the point P be (x, y, z), then the distances r₁ and r₂ are:

and

Therefore, the equation for potential becomes:

For an equipotential surface of zero potential, V = 0;

Squaring both sides, we have

Taking the –ve sign, as the +ve sign would give d=0 which is not true;

Therefore, the equation of equipotential surface for zero potential is a plane with equation x = 0, which is the mid-point between the charges as shown.