Question

A long straight wire is turned into a loop of radius $R=10cm$, as shown. If a current of $8A$ is passed through the loop, find the magnetic field at the centre C of the loop.

Answer 1

The magnetic field at C due to straight conductor is $B_1$

$B_1=\frac{{\mu }_{\circ }}{4\pi }\cdot \frac{2i}{r}=\frac{{\mu }_{\circ }}{4\pi }\cdot \frac{2\times 8}{10}=\frac{{\mu }_{\circ }}{4\pi }\cdot \frac{16}{10}$

The magnetic field at C due to circular coil is

$\begin{array}{c}{B}_2=\frac{{\mu }_{\circ }}{4\pi }\cdot \frac{2\pi i}{r}=\frac{{\mu }_{\circ }}{4\pi }\cdot \frac{2\pi 8}{10}=\frac{{\mu }_{\circ }}{4\pi }\cdot \frac{16\pi }{10}\\ B=B_2-B_1=\frac{{\mu }_{\circ }}{4\pi }\cdot \frac{16}{10}\left(\pi -1\right)T\end{array}$