Question

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.

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 1

Correct Answer - A::B::C
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.