Point charges -3 Q ,- q , 2 q and 2 Q are placed, one at each corner of a square. The relation between Q and q for which the potential at the centre of the square is zero is

Step-by-step solution

Let the side length of the square be a . The distance from each corner to the center of the square is r = a 2 . The electric potential V at the center due to a point charge q_i at distance r is given by V_i = k q_i r , where k = 1 4 ₀ . The total potential at the center is the sum of the potentials due to the four charges -3Q, -q, 2q, 2Q placed at the corners: V_ total = k r [(-3Q) + (-q) + (2q) + (2Q)] Setting the total potential to zero: k r [-3Q + 2Q - q + 2q] = 0 Since k r 0 , we have: -Q + q = 0 Q = q Answer: