Question

The figures 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)

• A. Both charges execute simple harmonic motion
• B. Charge $–q$ executes simple harmonic motion while charge $+q$ continues moving in the direction of its displacement
• C. Charge $+q$ executes simple harmonic motion while charge $–q$ continues moving in the direction of its displacement
• D. Both charges will continue moving in the direction of their displacement

Answer 1

The correct option is C Charge $+q$ executes simple harmonic motion while charge $–q$ continues moving in the direction of its displacement

As the ${}^{\prime }{+}^{\prime }$ charge is moved in $+x$-direction, it will experience a greater repulsion in $x$-direction while ${}^{\prime }{–}^{\prime }$ charge will be attracted.