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The Earth'S Magnetic Field at the Equator is Approximately 0.4 G. Estimate the Earth'S Magnetic Dipole Moment. - Physics

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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.

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Solution

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

`B=(mu_0M)/(4pid^3)`

where

d=R=Radius of the Earth

μ0=Absolute magnetic permeability of free space

M =Earth's dipole moment

Given:B=0.4 G=0.4×104 T

`mu_0/(4pi)=10^(-7) W_bA^(-1) m^(-1)`

`d=6400 km=6400000 m=6.4×10^6 m`

`∴M=(Bd^3)/(10^(−7))`

`⇒M=((0.4xx10^(−4))(6.4xx10^6)^3)/10^(−7)`

M=1.05×1023 A m2

Concept: Current Loop as a Magnetic Dipole and Its Magnetic Dipole Moment
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