Question

Two large insulating plates having surface charge densities $+\sigma$ and $-\sigma$ are fixed at a distance $d$ from each other. A small test charge $q$ of mass $m$ is attached to two identical springs as shown in the figure. The charge $q$ is now released from rest with springs in natural length. Then $q$ will (neglect gravity)

• A. perform SHM with angular frequency $\sqrt{\frac{k}{m}}$
• B. perform SHM with amplitude $\frac{\sigma q}{2k{ϵ}_0}$
• C. not perform SHM but will have a periodic motion
• D. remain stationary

Answer 1

Answer: (B)

Electric field between plates is uniform hence electrostatic force due to this field is constant. Angular frequency does not change by constant force equilibrium position will be at the point where $2k{x}_0=q\times \frac{\sigma }{{\in }_0};x_0=\frac{\sigma q}{2k{\in }_0}$
$x_0$ is also the amplitude of oscillation