Question

If earth is assumed to contain a magnetic dipole at its centre find its magnetic moment. Given that the magnetic field at a point on equator is $3.1\times {10}^{-5}$T and the radius of earth is $6400$km.

• A. $4.06\times {10}^{22}$ $A{m}^2$
• B. $8.13\times {10}^{22}A/m^2$
• C. $16.26\times {10}^{22}A{m}^2$
• D. $4.06\times {10}^{16}A/m^2$

Answer 1

The correct option is A $4.06\times {10}^{22}$ $A{m}^2$

Magnetic field due to a bar magnet on axial line is given by

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

where M=magnetic moment

as $r=6400km=6400\ast {10}^{3}m$

$\therefore 3.1\ast {10}^{-5}={10}^{-7}\ast \frac{2\ast M}{(6400\ast {10}^3)}$

$\therefore M=4.06\times {10}^{22}A{m}^2$