The figure below depict two situations in which two infinitely long static line charges of constant positive line charge density `lambda` 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)

Options

A. both charges execute simple harmonic motion.
B. both charge will continue moving in the direction of their displacement.
C. charge `+q` execute simple harmonic motion while charge `-q` continues moving in the direction of its displacement.
D. charge `-q` execute simple harmonic motion while charge `+q` continues moving in the direction of its displacement.

Answer

C

Explanation

Refer to Figs. (a) and (b), when point charges `+q` and `-q` are displaced a little towards positive x-direction, then `+ q` charge will experience resisting force which will tend to bring it back to its original position. As a result of it the charge `+q` wil execute `SHM`. The charge `-q` will

experience a force in the direction of displacement, hence charge `-q` will move in that direction. Therefore, option (C) is true.