Electrostatics 7 Question 6
6. 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 statements 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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Solution:
- At the shown position, net force on both charges is zero. Hence they are in equilibrium. But equilibrium of $+q$ is stable equilibrium. So, it will start oscillations when displaced from this position. These small oscillations are simple harmonic in nature. While equilibrium of $-q$ is unstable. So, it continues to move in the direction of its displacement.
