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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.
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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=0.4×10−4 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
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