Question

A ring of radius r is uniformly charged with charge $q$ . If the ring is rotated about it's axis with angular frequency $\omega$, then the magnetic induction at its centre will be-

• A. ${10}^{-1}\times \frac{\omega }{qr}$
• B. ${10}^{-7}\times \frac{9}{\omega r}$
• C. ${10}^{-7}\times \frac{r}{q\omega }$
• D. ${10}^{-7}\times \frac{q\omega }{r}$

Answer 1

The correct option is D ${10}^{-7}\times \frac{q\omega }{r}$

$\begin{array}{c}T=\frac{2\pi }{w}\\ i=\frac{qw}{2\pi }\\ B=\frac{{\mu }_{0}i}{2r}=\frac{{\mu }_0}{2r}\times \frac{qw}{2\pi }\\ ={10}^{-7}\times \frac{qw}{r}\\ Hence,\\ optionDiscorrectanswer.\end{array}$