Physics - Magnetism Question with Solution | TestHub

Let the radius of the ring is$r$.

Charge on the ring,

$q=l\lambda =2\pi r\lambda \left[\because l=2\pi r\right]$

Current due to the rotation of the ring,

$i=\frac{q}{t}=\frac{2\pi r\lambda }{\frac{2\pi }{\omega }}\left[\because t=\frac{2\pi }{\omega }\right]$

$=\omega \lambda r$

$i=\omega \lambda r$...(i)

$\therefore$Magnetic field at the centre of the ring due to the rotation of the charged ring.

$B=\frac{{\mu }_0}{2}.\frac{i}{r}=\frac{{\mu }_0}{2}.\frac{{\omega \lambda r}_{ }}{r}$

$=\frac{{\mu }_0}{2}.\omega \lambda$[Using Eq. (i)]