Q. The unit vectors $\widehat{i},\widehat{\ j}$ and $\widehat{k}$ are as shown below. What will be the magnetic field at $O$ in the following figure
A) $\frac{\mu_{0}}{4\pi}\frac{i}{a}\left( 2 - \frac{\pi}{2} \right)\widehat{j}$
B) $\frac{\mu_{0}}{4\pi}\frac{i}{a}\left( 2 + \frac{\pi}{2} \right)\widehat{j}$
C) $\frac{\mu_{0}}{4\pi}\frac{i}{a}\left( 2 + \frac{\pi}{2} \right)\widehat{i}$
D) $\frac{\mu_{0}}{4\pi}\frac{i}{a}\left( 2 + \frac{\pi}{2} \right)\widehat{k}$
Explanation
(d) The field at $O$ due to $AB$ is $\frac{\mu_{0}}{4\pi}.\frac{i}{a}\widehat{k}$ and that due to $DE$ is also $\frac{\mu_{0}}{4\pi}.\frac{i}{a}\widehat{k}$
However the field due t $BCD$ is $\frac{\mu_{0}}{4\pi}.\frac{i}{a}\left( \frac{\pi}{2} \right)\widehat{k}$
Thus the total field at $O$ is $\frac{\mu_{0}}{4\pi}.\frac{i}{a}\left( 2 + \frac{\pi}{2} \right)\widehat{k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.