A thin ring of radius ' $R$ ' meter has charge ' $q$ ' coulomb uniformly spread on it. The ring rotates…
A thin ring of radius ' $R$ ' meter has charge ' $q$ ' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $f$ revolution/s. The value of magnetic induction in $\mathrm{Wb} \mathrm{m}{ }^{-2}$ at the center of the ring is ( $\mu_0=$ Permeability of free space)
$\frac{\mu_0 q \mathrm{f}}{2 \pi R}$
$\frac{\mu_0 q}{2 \pi R}$
$\frac{\mu_0 \mathrm{qf}}{2 \mathrm{R}}$
$\frac{\mu_0 \mathrm{q}}{2 \pi \mathrm{fR}}$
Solution
For circular coil of radius $\mathrm{R}$ carrying a current $\mathrm{I}$, the magnetic field at the center is given by
$B=\frac{\mu_0 I}{2 R}$
Here $\mathrm{I}=\mathrm{qf}$
$\therefore \mathrm{B}=\frac{\mu_0 \mathrm{qf}}{2 \mathrm{R}}$