Question

The wire shown in the figure carries a current of $40A$. The magnetic field at $O$ is $0.4mT$. If radius of the loop is $r=n\times {10}^{-3}\pi$ meters, find $n$.

Answer 1

As both AB and DE part of conductor when extended passes through origin and hence contribution of magnetic field due to those part will be zero.

Magnetic field due to circular path will be given by

$B=\left(\frac{{\mu }_{0}I}{2R}\right)\ast \frac{{270}^{\circ }}{{360}^{\circ }}$

$0.4\ast {10}^{-3}=\frac{4\pi \ast {10}^{-7}\ast 40\ast 3}{2\ast n\ast {10}^{-3}\pi \ast 4}$

$\therefore n=\frac{120\ast {10}^{-7}}{2\ast {10}^{-3}\ast 0.4\ast {10}^{-3}}$

$=15$