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
$B_{net}=\sqrt{B_1^2+B_2^2}$
$=\sqrt{{\left(\frac{2{\mu }_0\mathrm{M}}{4\pi {\mathrm{d}}^3}\right)}^2+{\left(\frac{{\mu }_0\mathrm{M}}{4\pi {\mathrm{d}}^3}\right)}^2}=\frac{{\mu }_0\mathrm{M}}{4\pi {\mathrm{d}}^3}(\sqrt{5})$