First slide

Earth's Magnetism

Question

If the angles of dip at two places are 30 and 45° respectively, then the ratio of horizontal components of earth's magnetic field at the two places assuming magnitude of total magnetic field of earth is same will be

Moderate

A

$\sqrt{3} : \sqrt{2}$
B

$1 : \sqrt{3}$
C

$1 : \sqrt{2}$
D

1 : 2

Solution

The horizontal components are
${(B_{H})}_{1} = {Bcosϕ}_{1}$ and ${(B_{H})}_{2} = {Bcosϕ}_{2}$
$∴ \frac{{(B_{H})}_{1}}{{(B_{H})}_{2}} = \frac{{cosφ}_{1}}{{cosφ}_{2}} = \frac{\cos 30}{\cos 45} = \frac{\sqrt{3}}{2} \times \sqrt{2}$
$= \frac{\sqrt{3}}{\sqrt{2}}$

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