Question

Consider the circular loop having current $i$ and with central point $O$. The magnetic field at the central point $O$ is

• A. $\frac{2\mu_0 i}{3\pi R}$ acting downward
• B. $\frac{5\mu_0i}{12R}$ acting downward
• C. $\frac{6\,\mu_0 i}{11 R}$ acting downward
• D. $\frac{3\mu_0 i}{7R}$ acting upward

Answer 1

Answer: (B)

$\frac{5\mu_0i}{12R}$ acting downward

Answer 2

The angle subtended by circular part of the conduction is $3 \pi / 2$ or $270^{\circ}$. The net magnetic field at point $O$ is $B_{\text {net }}=B_{1}+B_{2}$ where, $B_{1}=$ magnetic field due to arc $II$ and $B_{2}=$ magnetic field due to arc $I$ $\Rightarrow B_{\text {net }} =\frac{\mu_{0} i}{4 \pi \times 3 R} \times \frac{\pi}{2}+\frac{\mu_{0} i}{4 \pi R} \times 3 \frac{\pi}{2}$ $=\frac{5 \mu_{0} i}{12 R}$ ( downward ) .