A charge of +2q is fixed to one corner of a square, while a charge of -3q is fixed to the diagonally opposite corner. Expressed in terms of q, what charge should be fixed to the center of the square, so the potential is zero at each of the two empty corners?

Answer 1

Potential is a scalar, so you can just add all four contributions.

Vt= -3q/r + 2q/r + 2X/r=0

solve for charge X