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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 (figure). Then
- If q > 0 and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre.
- 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.
- If q < 0, it will perform SHM for small displacement along the axis.
- q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q > 0.
Options
a and b
b and c
c and d
a, b, c and d
Solution
a, b, c and d
Explanation:
The positive charge Q is uniformly distributed along the circular ring then electric field at the centre of the ring will be zero, hence no force is experienced by the charge if it is placed at the centre of the ring.
Now the charge is displaced away from the centre in the plane of the ring. There will be a net electric field opposite to displacement that will push back the charge towards the centre of the ring if the charge is positive. If the charge is negative, it will experience a net force in the direction of displacement and the charge will continue moving till it hits the ring. Also, this negative charge is in an unstable equilibrium.
Charge placed at the centre of the ring
The charge displaced away from the centre of the ring
The direction of the electric field on the axis of a positively charged ring is along the axis of the ring and away from the centre of the ring. If a negative charge is shifted away from the centre along the axis of the ring, charge will experience a net force towards the centre and return to the centre and will perform SHM for small displacement along the axis.
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