A positive charge `Q` is uniformly distributed along a circular ring of radius `R`. A small test charge `q` is placed at the centre of the ring.

Options

A. if `qgt0` and is displaced away from the centre in the place of the ring, it will be pushed back towards the centre.
B. if `qlt0` ad is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring.
C. if `qlt0`, it will perrform SHM for small displacement along the axis
D. q at the centre of the ring is in an unstable equilibrium within the plane of the ring for `qgt0`

Answer

A, B, C

Explanation

The positive cahrge Q is uniformly distributed at the outer surface of the enclosed sphere. Thus, electric field inside the sphere is zero.
So, the effect of electric field on charge q due to the positive charge Q is zero. ltBrgt Now, The only giverning factor is the attractive and repulsive forces between cahrges (Q and q) there are two cases arise.
Case I when cahrge qgt0 i.e., q is a positive cahrge, there creates a repulsive force between charge q and Q. ltBrgt The repulsive force of charge Q from all around the charge q will push it towards the centre if it is displaced from the centre of the ring. ltBrgt Case II when cahrge qlt0 i.e., q is a negative cahrge then there is an attractive force between charge Q and q. ltBrgt if q is shifted from the centre, then the positive charges nearer to this charge will attract it towards itself and charge q will nerver return to the centre.