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. 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

C

Explanation

`F_("rest") =(lambdaq)/(2pi epsi_(0) (l-x))-(lambdaq)/(2piepsi_(0) (l+x))`
`=(lambdaq(2x))/(2piepsi_(0)(l^(2)-x^(2))`

`rArr F_("rest") approx (lambdaqx)/(pi epsi_(0) l^(2))`
`rArr` It executes SHM.
`F_("rest") approx (-lambdaq)/(2pi epsi_(0) (l-x)) +(lambdaq)/(2pi epsi_(0) (l+x))`
`F_("rest") approx (-lambdaqx)/(pi epsi_(0) l^(2))`
`rArr` Force is towards right hence the particle keeps going towards right.