Charge $q$ is uniformly spread on a thin ring of radius $R$. The ring rotates about its axis with a uniform…

Charge $q$ is uniformly spread on a thin ring of radius $R$. The ring rotates about its axis with a uniform frequency $f \mathrm{~Hz}$. The magnitude of magnetic induction at the centre of the ring is
  1. $\frac{\mu_0 q f}{2 R}$
  2. $\frac{\mu_0 q}{2 f R}$
  3. $\frac{\mu_0 q}{2 \pi f R}$
  4. $\frac{\mu_0 q f}{2 \pi R}$

Solution

We know $\begin{array}{ll} B=\frac{\mu_0 i}{2 R} \\ q=i t \Rightarrow i=\frac{q}{t}=q f \quad\left[\because f=\frac{1}{t}\right] \\ B=\frac{\mu_0 q f}{2 R} \end{array}$ *

Asked in: NEET 2011 (Mains)

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