Question

The current in the wire shown in the figure is $(1 / \sqrt{2}) A$. The magnetic field at point $P$ is $k \times 10^{-5} T$. The value of $k$ is

Answer 1

The magnetic field at $P$ due to segments $A B$ and $E F$ are zero,
due to segments $B C$ and $D E$ are $\frac{\mu_{0} I}{4 \pi r}\left(\sin 45^{\circ}\right) \otimes$
each and due to segment $C D$ is $\frac{\mu_{0} I}{4 \pi r}\left(\sin 45^{\circ}+\sin 45^{\circ}\right) \otimes$,
where $r=1 \,cm$.

Net magnetic field $=\frac{\mu_{0} I}{4 \pi r}\left[2 \times \sin 45^{\circ}+2 \times \sin 45^{\circ}\right]$
$=\frac{10^{-7} \times(1 / \sqrt{2})}{10^{-2}} \times 2 \sqrt{2} $
$=2 \times 10^{-5} T$
$\therefore k=2$