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.

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.


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