A thin ring of radius ' $R$ ' carries a uniformly distributed charge. The ring rotates at constant speed '…

A thin ring of radius ' $R$ ' carries a uniformly distributed charge. The ring rotates at constant speed ' $N$ ' r.p.s. about its axis perpendicular to the plane. If ' $B$ ' is the magnetic field at the centre, the charge on the ring is ( $\mu_0=$ permeability of free space)
  1. $\frac{\mu_0 \mathrm{~N}}{2 \mathrm{RB}}$
  2. $\frac{\mathrm{RB}}{2 \mu_0^{\prime} \mathrm{N}}$
  3. $\frac{\mu_0 \mathrm{~N}}{\mathrm{RB}}$
  4. $\frac{2 R B}{\mu_0 \mathrm{~N}}$

Solution

A thin uniformly charged rotating ring acts like a current carrying coil. Magnetic field at the centre of current carrying coil, $B=\frac{\mu_0 I}{2 R}$
Current is given by, $\mathrm{I}=\mathrm{qN} \quad$ where N is revolutions per second. $\begin{array}{ll} \therefore & B=\frac{\mu_0 q N}{2 R} \\ \therefore & q=\frac{2 R B}{\mu_0 N} \end{array}$ ...[From(i)]

Asked in: MHT CET 2024 (03 May Shift 2)

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