Question

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density λ are kept parallel to each other. In their resulting electric field, point charges q and – q are kept in equilibrium between them. The point charges are confined to move in the x-direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is (are):

(a) Both charges execute simple harmonic motion.
(b) Both charges will continue moving in the direction of their displacement.
(c) Charge +q executes simple harmonic motion while charge -q continues moving in the direction of its displacement.
(d) Charge -q executes simple harmonic motion while charge +q continues moving in the direction of its displacement

Answer 1

As +q is displaced towards right, the repulsion of right side wire will dominate and the net force on +q will be towards left, and vice versa

Hence SHM
For –q, as it is displaced towards right the attraction of right side wire will dominate, which forces the -q charge to move in the same direction of displacement similarity for other side Hence it is not SHM.

Comments

Why do we use d plus x and d minus x in the first expression of restoring force

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It's not mentioned in the question that the charge is pushed to the right. Wouldn't the answer be different if they were both pushed to the left instead?