Oscillation of Charge in Ring Field – Rankers Physics
Topic: Electrostatics
Subtopic: Electric Field

Oscillation of Charge in Ring Field

Assertion (A): When a negative charge \(-q\) is released at a distance \(R\) from the centre and along the axis of a uniformly and positively charged fixed ring of radius \(R\), the negative charge does oscillation but not SHM.
Reason (R): The force on negative charge is always towards the centre of the ring but it is not proportional to the displacement from the centre of the ring.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true. The electric force on charge \(-q\) on the axis of a positively charged ring is a restoring force towards the center, causing oscillation. The force is \(F = \frac{kQqx}{(R^2+x^2)^{3/2}}\). This is not linearly proportional to \(x\) (displacement) unless \(x \ll R\), so it's not SHM. Reason (R) is true. The force is attractive (towards center) and indeed not proportional to \(x\). Reason (R) correctly explains Assertion (A).

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