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 gt 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 lt 0` and is displaced away from the centre in the plane of the ring, it will, it will never return to the centre and will continue moving till it his the ring.
C. If `q lt 0`, it will perform SHM for small displacement along the axis,
D. `q` at the centre of the ring is an unstable equilibrium within the plane of the ring for `q gt 0`.

Answer

A, B, C

Explanation

As is known from theory, 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 repusion 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. Choice (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 of the ring. Choice (b) is correct.
Along the axis of the ring, at a distnance `r` from the centre, `E = (Q r)/( 4pi in_(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. Choice (c ) is correct.