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 $B=\frac{{\mu }_{0}qf}{2R}$