Question

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. $\frac{{\mu }_0}{4\pi }\left(\sqrt{6}\right)\frac{M}{d^3}$
• B. $\frac{{\mu }_0}{4\pi }\left(\sqrt{2}\right)\frac{M}{d^3}$
• C. $\left(\frac{2{\mu }_0}{\pi }\right)\frac{M}{d^3}$
• D. $\frac{{\mu }_0}{4\pi }\left(\sqrt{5}\right)\frac{M}{d^3}$

Answer 1

The correct option is D $\frac{{\mu }_0}{4\pi }\left(\sqrt{5}\right)\frac{M}{d^3}$


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 $B_2=\frac{{\mu }_0}{4\pi }.\frac{M}{d^3}$
$\Rightarrow B_{net}=\frac{{\mu }_0}{4\pi }.\frac{\sqrt{5}M}{d^3}$