Q. A current loop consists of two identical semicircular parts each of radius $R$, one lying in the $x - y$ plane and the other in $x - z$ plane. If the current in the loop is $i$. The resultant magnetic field due to the two semicircular part at their common centre is
A) $\frac{\mu_{0}i}{2\sqrt{2}R}$
B) $\frac{\mu_{0}i}{2R}$
C) $\frac{\mu_{0}i}{4R}$
D) $\frac{\mu_{0}i}{\sqrt{2}R}$
Explanation
(a) $\overrightarrow{B} = {\overrightarrow{B}}_{1} + {\overrightarrow{B}}_{2}$
$\left| {\overrightarrow{B}}_{1} \right| = \left| {\overrightarrow{B}}_{2} \right| = \frac{\mu_{0}i}{4R}$
$\left| \overrightarrow{B} \right| = \sqrt{B_{1}^{2} + B_{2}^{2}}$
$\left| \overrightarrow{B} \right| = \frac{\mu_{0}i}{4R}\sqrt{2} = \frac{\mu_{0}i}{2\sqrt{2}R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.