First slide

Magnetism

Question

The magnetic moment of the assumed dipole at the earth’s center is $8 \times 10^{22} A m^{2}$ . The magnetic field B at the geomagnetic poles of the earth is $\frac{P \times 10^{15}}{R^{3}}$ .(where R is Radius of earth). Then the value of ‘P’ is___

Moderate

Solution

The geometric pole is at the end on position of the earth $B = \frac{μ_{0}}{4 π} . \frac{2 M}{d^{3}}$
$d = R; M = 8 \times 10^{22} A m^{2}; B = \frac{P \times 10^{15}}{R^{3}}$
$∴ B = \frac{10^{- 7} \times 2 \times 8 \times 10^{22}}{R^{3}}$
$\Rightarrow \frac{P \times 10^{15}}{R^{3}} = \frac{16 \times 10^{15}}{R^{3}} \Rightarrow P = 16.$

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