Question

The equatorial magnetic field of earth is $0.4$G. Then its dipole moment on equator is

• A. $1.05\times {10}^{23}A{m}^2$
• B. $2.05\times {10}^{23}A{m}^2$
• C. $1.05\times {10}^{21}A{m}^2$
• D. $2.05\times {10}^{21}A{m}^2$

Answer 1

Answer: (A)

$1.05\times {10}^{23}A{m}^2$

Assuming the Earth's magnetic field is due to a bar magnet at center of the Earth, held along the polar axis of Earth, the equatorial magnetic field of Earth is given by

$B=\frac{{\mu }_{0}M}{4\pi r^3}$

where,

$r=$ Radius of earth $=6400km=6.4\times {10}^{6}m$

$M=$ Earth's magnetic dipole moment

Given $B=0.4G=0.4\times {10}^{-4}T$

$\therefore M=\frac{B{r}^3}{\frac{{\mu }_o}{4\pi }}=\frac{(0.4\times {10}^{-4})(6.4\times {10}^6{)}^3}{{10}^{-7}}$

$\therefore M=1.05\times {10}^{23}A{m}^2$

So, option $A$ is correct