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 .The

Options

A. if q > 0, and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre.
B. if q < 0 and 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 q < 0 it will perform SHM for small displacement along the axis.
D. all of the above

Answer

D

Explanation

At the centre of the ring, E = 0 when a positive charge q gt 0 is displaced away from the centre in the plane of the ring, say to the right, force of repulsion on q, due to charge on right half increases and due to charge on left half decreases. Therefore, charge q is pushed back towards the centre. So option (a) is correct.
When charge q is negative (q lt 0), force is of attraction.
Therefore, charge q displaced to the right continues moving to the right till it hits the ring. Along the axis of the ring, at a distance r from the centre,
`E=(Qr)/(4piepsilon_(0)(r^(2)+a^(2))^(3//2))`
If charge q is negative (q lt 0), it will perform SHM for small displacement along the axis.