Question

If the earth's magnetic field has a magnitude $3.4\times {10}^{-5}T$ at the magnetic equator of the earth, what would be its value at the earth's geomagnetic poles?

Answer 1

$\overrightarrow{B}=3.4\times {10}^{-5}T$

Given $\frac{{\mu }_0}{4\pi }\frac{M}{R^3}=3.4\times {10}^{-5}$

$M=\frac{3.4\times {10}^{-5}\times R^3\times 4\pi }{4\pi \times {10}^{-7}}=3.4\times {10}^2{R}^3$

$\overrightarrow{B}$ at poles $=\frac{{\mu }_0}{4\pi }\frac{2M}{R^3}=6.6\times {10}^{-5}T$