Question

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

• A. $\frac{{\mu }_{0}I}{4R}\left(1+\frac{\sqrt{2}}{\pi }\right)$
• B. $\frac{{\mu }_{0}I}{4R}\left(1-\frac{2}{\pi }\right)$
• C. $\frac{{\mu }_0\mathrm{I}}{2\mathrm{R}}\left(1+\frac{\sqrt{2}}{\pi }\right)$
• D. $\frac{{\mu }_{0}I}{4R}\left(1+\frac{2\sqrt{2}}{\pi }\right)$

Answer 1

Answer: (A)

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