Question

A current-carrying loop is shown in the figure. The magnitude of the magnetic field produced at a point $O$ is

• A. $\frac{\mu_0 I}{4 R}\left(1+\frac{\sqrt{2}}{\pi}\right)$
• B. $\frac{\mu_0 I}{4 R}\left(1-\frac{2}{\pi}\right)$
• C. $\frac{\mu_0 \mathrm{I}}{2 \mathrm{R}}\left(1+\frac{\sqrt{2}}{\pi}\right)$
• D. $\frac{\mu_0 I}{4 R}\left(1+\frac{2 \sqrt{2}}{\pi}\right)$

Answer 1

Answer: (A)

$\mathrm{B}_0=\frac{\mu_0 \mathrm{I}}{2 \mathrm{R}} \times \frac{1}{2}+4 \times \frac{\mu_0 \mathrm{I}}{4 \pi \times(2 \mathrm{R})} \times \frac{1}{\sqrt{2}}$
$\mathrm{B}_0=\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}}\left(1+\frac{\sqrt{2}}{\pi}\right)$