Question

A uniformly charged ring of radius R carrying q is rotating with angular speed $\omega$. The magnetic field at the centre of ring is:

• A. $\frac{{\mu }_{o}q\omega }{2\pi R}$
• B. $\frac{{\mu }_{o}q\omega }{4\pi R}$
• C. $\frac{{\mu }_{o}q\omega }{8\pi R}$
• D. Zero

Answer 1

The correct option is B $\frac{{\mu }_{o}q\omega }{4\pi R}$

Given,

Charge$q$ , rotating in circular motion of radius $R$

Linear charge density,$\lambda =\frac{q}{2\pi R}$

Time period, $T=2\pi /\omega$

Current in circular motion, $I=\frac{q}{T}=\frac{q\omega }{2\pi }$

Magnetic field at center, $B={\mu }_{0}I/2R$

$B=\frac{{\mu }_o\omega }{2}\cdot \frac{q}{2\pi R}=\frac{{\mu }_{o}q\omega }{4\pi R}$

Hence, magnetic field at center $\frac{{\mu }_{o}q\omega }{4\pi R}$