Q. Two identical short bar magnets, each having magnetic moment $M$, are placed a distance of $2d$ apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is
A) $\frac{\mu_{0}}{4\pi}\left( \sqrt{2} \right)\frac{M}{d^{3}}$
B) $\frac{\mu_{0}}{4\pi}\left( \sqrt{3} \right)\frac{M}{d^{3}}$
C) $\left( \frac{2\mu_{0}}{\pi} \right)\frac{M}{d^{3}}$
D) $\frac{\mu_{0}}{4\pi}\left( \sqrt{5} \right)\frac{M}{d^{3}}$
Explanation
(d) At point $P$ net magnetic field $B_{net} = \sqrt{B_{1}^{2} + B_{2}^{2}}$
Where $B_{1} = \frac{\mu_{0}}{4\pi}.\frac{2M}{d^{3}}$ and $B_{2} = \frac{\mu_{0}}{4\pi}.\frac{M}{d^{3}}$
$\Rightarrow B_{net} = \frac{\mu_{0}}{4\pi}.\frac{\sqrt{5}M}{d^{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.