Question

The Earth’s magnetic field at the Equator is approximately 0.4 G. Estimate the Earth’s magnetic dipole moment. Given : Radius of the Earth = 6400 km.

Answer 1

Given:-

Magnetic filed of the earth

$= 0.4\:G$

$= 0.4 \times 10 ^{ - 4} \:G$

Equatorial magnetic field of the earth is given by,

$B = \frac{μ_{0}M}{4\pi \: d^{3} }$

Where,

$d = 6400\:km$

$d = 6.4 \times 10^{6} m$

Therefore,

Earth's magnetic dipole moment is given by,

$M = \frac{Bd^{3} }{10 ^{ - 7} }$

$M = \frac{(0.4 \times 10 ^{ - 4}) \times (6.4 \times 10 ^{6})^{3} }{10^{ - 7} }$

$M = 1.05 \times 10^{23} Am^{2}$
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$\bold{Final\:answer:-}$

$M = 1.05 \times 10^{23} Am^{2}$

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