Two large non conducting plates having surface charge densities `+sigma` and `-sigma` respectively, are fixed `d` distnce apart. A small test charge `q` of mass `m` is attached to two non conducting springs each of spring constant `k` as shown in the figure. The sum of lengths of both springs in underformed state is `d`. The charge `q` is released from rest with both the springs nondeformed. then charge `q` will (neglect gravity)

Options

A. perform SHM with angular frequence `sqrt(k/m)`
B. not perform SHM with amplitude `(sigma q)/(2kepsilon_(0))`
C. not perform SHM but will have a periodic moton
D. remain stationary

Answer

B

Explanation

Eelctric fiedl between plastes 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 `2kx_(0)=qxx(sigma)/(in_(0)),x_(0)=(sigmaq)/(2k in_(0))`
`x_(0)` is also the amplitude of oscillation.