Question

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

• A. $\frac{{\mu }_{0}q\omega }{4\pi r}$
• B. $\frac{{\mu }_{1}q\omega }{4\pi r}$
• C. $\frac{{\mu }_0{q}_1\omega }{4\pi r}$
• D. $\frac{{\mu }_{2}q\omega }{4\pi r}$

Answer 1

The correct option is A $\frac{{\mu }_{0}q\omega }{4\pi r}$

$\text{Solution}:$

Current in the ring

$I=\frac{\omega q}{2\pi }$

Magnetic field

$B=\frac{{\mu }_{0}I}{2r}=\frac{{\mu }_0\omega q}{2\pi \times 2r}$

$⟹B=\frac{{\mu }_0\omega q}{4\pi r}$

$\text{Hence A is the correct option}$