Question

Three short bar magnets are arranged as shown. Find resultant magnetic induction at the point O.

Answer 1

A Bar magnet are short, we can use appropriate formulaes.

Magnetic field an axial line

$B_a=\frac{{\mu }_0}{4\pi }\frac{2M}{r^3}$

magnetic field on equitorial line

$B_e=\frac{{\mu }_0}{4\pi }\frac{M}{r^3}$

$\overrightarrow{B_{net}}=\overrightarrow{B_1}+\overrightarrow{B_2}+\overrightarrow{B_3}$

$=\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}\hat{i}+\frac{{\mu }_0}{4\pi }\frac{2\ast 2M}{d^3}\widehat{-i}+\frac{{\mu }_0}{4\pi }\frac{3M}{d^3}\widehat{-i}$

$=\frac{{\mu }_{0}M}{4\pi d^3}[2-4-3]\hat{i}$

$=\frac{-5{\mu }_{0}M}{4\pi d^3}\hat{i}$