Moving Charges and Magnetism - Result Question 38

39. Charge $q$ is uniformly spread on a thin ring of radius $R$. The ring rotates about its axis with a uniform frequency $f Hz$. The magnitude of magnetic induction at the centre of the ring is

[2011M, 2010]

(a) $\frac{\mu_0 q f}{2 R}$

(b) $\frac{\mu_0 q}{2 f R}$

(c) $\frac{\mu_0 q}{2 \pi f R}$

(d) $\frac{\mu_0 q f}{2 \pi R}$

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Answer:

Correct Answer: 39. (a)

Solution:

  1. (a) When the ring rotates about its axis with a uniform frequency $f Hz$, the current flowing in the ring is

$I=\frac{q}{T}=q f$

Magnetic field at the centre of the ring is

$B=\frac{\mu_0 I}{2 R}=\frac{\mu_0 q f}{2 R}$