A charged particle having some mass is resting in equilibrium at a height H above the centre of a uniformly charged non conducting horizontal ring of radius R. The force of gravity acts downwards. The equilibrium of the particle will be stable:

Options

A. for all values of H
B. only if `H gt R/sqrt(2)`
C. only if `H lt R/sqrt(2)`
D. only if `H=R/sqrt(2)`

Answer

B

Explanation

`mg=qxx(KQH)/((R^(2)+H^(2))^(3//2))`
The field due to ring on its axis will be maximum at `H= pm R/sqrt(2)` i.e. above that point `qE` force will decrease and resultant force becomes in downward direction (equilibrium position) and also in same way for below point.