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Question:

The magnetic field of earth at the equator is approximately 4 × 10⁻⁵ T. The radius of earth is 6.4 × 10⁶ m. Then the dipole moment of the earth will be nearly of the order of :

10²³Am²

10¹⁰Am²

10²⁰Am²

10¹⁶Am²

Solution:

Answer is A
We know that, magnetic field of earth is
B = μ₀/4π(2M/r³)
Dipole moment, M = B × 4πr³/2μ₀
Assuming μ₀/4π = 10⁻⁷
M = (4 × 10⁻⁵) × 4π(6.4 × 10⁶)³/2 × 10⁻⁷
M ≈ 10²³ Am²