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Two large on conducting plates having surface charge densities $+ σ$ and $- σ$ , respectively, are fixed ‘d’ distance apart. A small test charge q of mass m is attached to two non – conducting identical springs of spring constant k as shown in the adjacent fig. The charge q is now released from rest with springs in natural length. Then q will [neglect gravity]

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perform SHM with angular frequency $\sqrt{\frac{2 k}{m}}$

not perform SHM, but will have a periodic motion if charges are removed on plates as well as on m

remain stationary

perform SHM with amplitude $\frac{σq}{2 k \in_{0}}$

answer is A, B.

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Detailed Solution

A = deformation from equilibrium state

$2 kA = \frac{σ}{ϵ_{0}} q ∴ A = \frac{σq}{2 {kϵ}_{0}}$

Springs are connected in parallel k_eq = 2k

Angular frequency $= \sqrt{\frac{2 k}{m}}$

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