Question

A current $I$ flows in an infinitely long wire with corss section in the form of a semi-circular ring of raidus $R$. The magnitude of the magnetic induction along its axis is

• A. $\frac{\mu_{0} I}{4 \pi R}$
• B. $\frac{\mu_{0} I}{\pi^{2} R}$
• C. $\frac{\mu_{0} I}{2 \pi^{2} R}$
• D. $\frac{\mu_{0} I}{2 \pi R}$

Answer 1

Answer: (B)

$B=\int d B \sin \theta$
$B=\int \frac{\mu_{0} d i}{2 \pi R} \sin \theta$
$=\frac{\mu_{0}}{2 \pi R}\left(\frac{i}{\pi R}\right) R \int\limits_{0}^{\pi} \sin \theta d \theta$
$=\frac{\mu_{0} i}{\pi^{2} R}$