Question

The earth’s magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to $8 \times 10^{22} \, Am^2$, the value of earth’s magnetic field near the equator is close to (radius of the earth = $6.4 \times 10^6$ m)

• A. 0.6 Gauss
• B. 1.2Gauss
• C. 1.8 Gauss
• D. 0.32 Gauss

Answer 1

Answer: (A)

Given $M = 8 \times10^{22} Am^{2}$
$ d = R_{e} = 6.4 \times10^{6}m $
Earth’s magnetic field, $B = \frac{\mu_{0}}{4\pi} . \frac{2M}{d^{3}}$
$ = \frac{4\pi\times10^{-7}}{4\pi} \times\frac{ 2 \times 8 \times10^{22}}{\left(6.4 \times10^{6}\right)^{3}} $
$\cong $ 0.6 Gauss