Two large non-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 identicals springs, each of spring constant 2K as shown in the fig. The charge q is now released from rest with springs in natural length. Then q will (neglect Gravity)

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Perform SHM with angular frequency $2 \sqrt{\frac{K}{m}}$

Perform SHM with amplitude $\frac{σq}{4 K \in_{0}}$

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

Remain stationary

answer is A, B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Eelctrostatic force doesn’t effect time period $w = \sqrt{\frac{keff}{m}} = \sqrt{\frac{4 k}{m}} = 2 \sqrt{\frac{K}{m}}$
Charge is at rest at extreme position $F = qE = q [\frac{σ}{2 \in_{0}} + \frac{σ}{2 \in_{0}}] = \frac{qσ}{\in_{0}}$
$4 {kx}_{0} = \frac{qσ}{\in_{0}}$
Amplitude $x_{0} = \frac{qσ}{4 k \in_{0}}$