Question

In the given figure magnetic field at the center of ring $O$ is $\frac{8}{\sqrt{2}}T$ . Now it is turned through $90^\circ $ about $xx'$ axis, so that two semicircular parts are mutually perpendicular. The new value of magnetic field (in Tesla) at centre is $\sqrt{n}$ . Find $n$ .

Answer 1

Given, $\frac{\mu _{0} i}{2 R}=\frac{8}{\sqrt{2}}T$
In $2^{\text {nd }}$ case,
$ |\vec{B}|=\sqrt{\left(\frac{\mu_0 i}{4 R}\right)^2+\left(\frac{\mu_0 i}{4 R}\right)^2}=\frac{\mu_0 i}{2 \sqrt{2} R}=4 \mathrm{~T} $