Question

A magnetic plane of magnetic moment $0.72A{m}^2$ is placed horizontally with the north pole pointing towards south. Find the position of the neutral point if the horizontal component of the earth's magnetic field is $18\mu T$

Answer 1

When the magnet is such that its North faces the geographic south of earth. The neutral point lies along the axial line of the magnet.

$\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}=18\times {10}^{-6}\Rightarrow \frac{{10}^{-7}\times 2\times 0.72}{d^3}=18\times {10}^{-6}\Rightarrow d^3=\frac{2\times 0.7\times {10}^{-7}}{18\times {10}^{-6}}$

$\Rightarrow d={\left(\frac{8\times {10}^{-9}}{{10}^{-6}}\right)}^{1/2}=2\times {10}^{-1}m=20cm$