Four point charges −Q, −q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is ?

Four point charges −Q, −q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is ?

(a) \( Q = -q \)

(b) \( Q = -\frac{1}{q} \)

(c) \( Q = q \)

(d) \( Q = \frac{1}{q} \)

Answer :  (a) \( Q = -q \)

\(-\frac{kQ}{r} - \frac{kq}{r} + \frac{k \cdot 2Q}{r} + \frac{k \cdot 2q}{r} = 0\)

\(Q + q = 0\)

\(Q = -q\)