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5.Magnetism and Matter
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The earth’s magnetic field at the equator is approximately $0.4 \;G$. Estimate the earth’s dipole moment.
A
$5.67 \times 10^{20}\; A m ^{2}$
B
$1.38 \times 10^{22}\; A m ^{2}$
C
$6.022 \times 10^{24}\; A m ^{2}$
D
$1.05 \times 10^{23}\; A m ^{2}$
Solution
the equatorial magnetic field is,
$B_{E}=\frac{\mu_{0} m}{4 \pi r^{3}}$
We are given that $B_{E} \sim 0.4 G =4 \times 10^{-5} T .$
For $r,$ we take the radius of the earth $6.4 \times 10^{6} m .$ Hence,
$m=\frac{4 \times 10^{-5} \times\left(6.4 \times 10^{6}\right)^{3}}{\mu_{0} / 4 \pi}$$=4 \times 10^{2} \times\left(6.4 \times 10^{6}\right)^{3} \;\;\left(\mu_{0} / 4 \pi=10^{-7}\right)$
$=1.05 \times 10^{23} Am ^{2}$
This is close to the value $8 \times 10^{22}\; A m ^{2}$ quoted in geomagnetic texts.
Standard 12
Physics
