The earth’s magnetic field at the equat | vedclass

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Question

the equatorial magnetic field is,

$B_{E}=\frac{\mu_{0} m}{4 \pi r^{3}}$

We are given that $B_{E} \sim 0.4 G =4 	imes 10^{-5} T .$

For $r,$ w

Vedclass · Accepted Answer

$1.05 	imes 10^{23}\; A m ^{2}$

Vedclass · Answer

the equatorial magnetic field is,

$B_{E}=\frac{\mu_{0} m}{4 \pi r^{3}}$

We are given that $B_{E} \sim 0.4 G =4 	imes 10^{-5} T .$

For $r,$ we take the radius of the earth $6.4 	imes 10^{6} m .$ Hence,

$m=\frac{4 	imes 10^{-5} 	imes\left(6.4 	imes 10^{6}ight)^{3}}{\mu_{0} / 4 \pi}$$=4 	imes 10^{2} 	imes\left(6.4 	imes 10^{6}ight)^{3} \;\;\left(\mu_{0} / 4 \pi=10^{-7}ight)$

$=1.05 	imes 10^{23} Am ^{2}$

This is close to the value $8 	imes 10^{22}\; A m ^{2}$ quoted in geomagnetic texts.

The earth’s magnetic field at the equator is approximately $0.4 \;G$. Estimate the earth’s dipole moment.

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