Question

Consider the situation in the figure. The work done in taking a point charge from P to A is W_A, from P to B is W_B and from P to C is W_C.
(a) W_A < W_B < W_C
(b) W_A > W_B > W_C
(c) W_A = W_B = W_C
(d) None of these

Answer 1

(c) W_A = W_B = W_C

Points A, B and C lie at the same distance from the charge q, i.e. they are lying on an equipotential surface. So, work done in moving a charge from A to B (W_AB) or B to C (W_BC) is zero.
Hence, work done in bringing a charge from P to A = W_A,
from P to B, W_B = W_A+W_AB = W_A
and from P to C, W_C = W_A + W_AB + W_BC = W_A​

Hence, W_A = W_B = W_C