Question

A thin ring of radius R metre 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 $ \text{Wb}{{\text{m}}^{-2}} $ at the centre of the ring is

• A. $ \frac{{{\mu }_{0}}qf}{2\pi R} $
• B. $ \frac{{{\mu }_{0}}q}{2\pi fR} $
• C. $ \frac{{{\mu }_{0}}q}{2fR} $
• D. $ \frac{{{\mu }_{0}}qf}{2R} $

Answer 1

Answer: (C)

The magnetic field at the centre of the circle $ =\frac{{{\mu }_{0}}}{4\pi }\times \frac{2\pi i}{R}=\frac{{{\mu }_{0}}}{2}\frac{(q)}{Rt} $ We have frequency $ f=\frac{1}{T} $ $ \therefore $ The magnetic field $ B=\frac{{{\mu }_{0}}qf}{2R} $