Question

Two identical short bar magnets each having magnetic moment $M$ are placed at a distance of $2d$ with their axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

• A. $\frac{\sqrt{2} \mu _{0} M}{4 \pi d^{3}}$
• B. $\frac{\sqrt{3} \mu _{0} M}{4 \pi d^{3}}$
• C. $\frac{\mu _{0} M}{2 \pi d^{3}}$
• D. $\frac{\sqrt{5} \mu _{0} M}{4 \pi d^{3}}$

Answer 1

Answer: (D)

At
magnetic field is a vector quantity. at point p two magnetic field are acting at 90^o
$ \, B_{n e t}=\sqrt{B_{1}^{2} + B_{2}^{2}}$
$=\sqrt{\left(\frac{2 \mu_0 \mathrm{M}}{4 \pi \mathrm{d}^3}\right)^2+\left(\frac{\mu_0 \mathrm{M}}{4 \pi \mathrm{d}^3}\right)^2}=\frac{\mu_0 \mathrm{M}}{4 \pi \mathrm{d}^3}(\sqrt{5})$