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

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

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

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

= $3.4\times {10}^2{R}^3$

$\overrightarrow{B}atpoles=\frac{{\mu }_0}{4\pi }\times \frac{2M}{R^3}$

= $\frac{{10}^{-7}\times 2\times 3.4\times {10}^2{R}^3}{R^3}$

= $6.8\times {10}^{-5}$ T