Question

A ring of radius $\left(R\right)$ carries a uniformly distributed charge $+Q$. A point charge $-q$ is placed on the axis of the ring at a distance $2R$ from the centre of the ring and released from rest. The particle

• A. stays in rest
• B. executes simple harmonic motion
• C. executes oscillation but not SHM
• D. moves to the centre of ring immediately and stays there

Answer 1

The correct option is C executes oscillation but not SHM

Net force due to ring at a point on axis for a particle having charge $-q$ is $F=\frac{Qqx}{4\pi {ϵ}_0(R^2+x^2{)}^{3/2}}$, acting towards centre of the ring.

Since the force is attractive, the particle will carryout a periodic motion with ring's centre as its mean position.

As $F=\frac{-KQqx}{(x^2+R^2{)}^{3/2}}$ is not of form $F=-kx$ , oscillation is not in SHM.