Physics Electrostatics Potential & Capacitance JEE (Main) / AIEEE Problems Previous Years - ( Capacitance ) MCQ (Single Correct)

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.

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The correct answer is:
C

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

F restoring = q

F restoring =

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

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