What point charges, all having the same magnitude, would you place at the corners of a square (one charge per corner), so that both the electric field and the electric potential (assuming a zero reference value at infinity) are zero at the center of the square?

Explanation:

Let ABCD be the square having A,B,C,D being consecutive corners . If we place equal positive charges on each corner , net electrical field will be zero at the center but potential at the center will not be zero .

If we place equal positive charges at opposite corner and equal negative charges on other two corners , both net field and net potential at the center will be zero. Two equal positive charges at opposite corner will create net zero field. Similarly , Two equal negative charges will create zero field at the center. Two equal positive and two equal negative charge will create zero potential at the center.