First slide

Magnetic elements of Earth

Question

A dip needle lies initially in the magnetic meridian when it shows an angle of dip $' θ'$ at the place. The dip circle is rotated through an angle $' x'$ in the horizontal plane and then it shows an angle of dip $θ^{1}$ . Then, $\tan θ^{1} / \tan θ$ is

Moderate

A

$1 / \cos x$
B

$1 / \sin x$
C

$1 / \tan x$
D

$\cos x$

Solution

As the dip circle is rotated , we have to take the component of $B_{H}$
$I n i t i a l l y, \tan θ = \frac{B_{v}}{B_{H}}$
$F i n a l l y, \tan θ^{1} = \frac{B_{v}}{B_{H} \cos x} D i v i d i n g, w e g e t$
$\frac{\tan θ}{\tan θ^{1}} = \frac{B_{v} / B_{H}}{B_{v} / B_{H} \cos x}$
$\Rightarrow \frac{\tan θ}{\tan θ^{1}} = \cos x$
$\Rightarrow \frac{\tan θ^{1}}{\tan θ} = \frac{1}{\cos x}$

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