Question

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

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

Answer 1

Answer: (D)

$\left(\sqrt{5}\right)\frac{{\mu }_0}{4\pi }\frac{M}{d^3}$

$B_1=\frac{2M{\mu }_0}{4\pi d^3}$ at axial position
$B_2=\frac{M{\mu }_0}{4\pi d^3}$ at equatorial position
$B_{Net}=\sqrt{B_1^2+B_2^2}$
$=\frac{M{\mu }_0}{4\pi d^3}\sqrt{5}$