Assume the magnetic moment of the dipole at the earth's centre is 8.0 × 10^ 22 A m^2 . Determine the magnetic field B at the earth's geomagnetic poles. The radius of the earth is 6400 km .

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 6.1 × 10^ -5 T

The magnetic field at the geomagnetic poles (which lie on the axial line of the earth's magnetic dipole) is given by:

B = \dfrac{\mu_0}{4\pi} \dfrac{2M}{R^3}

Given:

M = 8.0 \times 10^{22} \text{ A m}^2

R = 6400 \text{ km} = 6.4 \times 10^6 \text{ m}

\dfrac{\mu_0}{4\pi} = 10^{-7} \text{ T m A}^{-1}

Substituting the values:

B = 10^{-7} \times \dfrac{2 \times 8.0 \times 10^{22}}{(6.4 \times 10^6)^3}

B = 10^{-7} \times \dfrac{16.0 \times 10^{22}}{262.144 \times 10^{18}}

B = 10^{-7} \times 0.061 \times 10^4

B = 6.1 \times 10^{-5} \text{ T}

Assume the magnetic moment of the dipole at the earth's centre is...

Options

Correct answer

Step-by-step solution

More from Permanent Magnets