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 dispacement about their equilibrium positions, then the correct ststement(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 haramonic motion while charge −q continues moving in the direction of its displacement. (D) Charge -q executes simple haramonic motion while charge +q continues moving in the direction of its displacement.
(A)Both charges execute simple harmonic motion.
(B)Both charges will continue moving in the direction of their displacement.
(C)Charge +q executes simple haramonic motion while charge −q continues moving in the direction of its displacement.✓ Correct
(D)Charge -q executes simple haramonic motion while charge +q continues moving in the direction of its displacement.
Answer: (C)
Solution
For the +q charge: When displaced towards the right, the repulsion from the right wire dominates, creating a restoring force towards the left (equilibrium position). Similarly, displacement to the left creates a force to the right. The net force is F≈d24kλqx, which is proportional to displacement and directed towards equilibrium — this is SHM.
For the −q charge: When displaced towards the right, the attraction from the right wire dominates, pulling it further right (away from equilibrium). Similarly, displacement to the left pulls it further left. The force is in the same direction as displacement — this is unstable equilibrium, and the charge continues moving in the direction of displacement.
Therefore, +q executes SHM while −q continues moving in the direction of its displacement.
JEE Advanced · 2015 · 24 May 2015 · Paper 1 · One or more correct options
