Question

The earth's magnetic field at the equator is approximately $0.4G$. The earth's dipole moment is :
$(R_e=6.4\times {10}^{6}m)$

• A. $4\times {10}^{2}A{m}^2$
• B. $1.05\times {10}^{23}A{m}^2$
• C. $4\times {10}^{-5}A{m}^2$
• D. $1.05\times {10}^{-20}A{m}^2$

Answer 1

The correct option is B $1.05\times {10}^{23}A{m}^2$

The equatorial magnetic field is:
$B=\frac{{\mu }_0}{4\pi }\frac{m}{r^3}$
Given,
$B=0.4G=0.4\times {10}^{-4}T$
Radius of earth $r=6.4\times {10}^{6}m$
$\therefore m=\frac{B}{\frac{{\mu }_0}{4\pi }}{r}^3=\frac{0.4\times {10}^{-4}}{{10}^{-7}}(6.4\times {10}^6{)}^3=104.9\times {10}^{21}=1.05\times {10}^{23}A{m}^2$