Question

A dip needle lies initially in the magnetic meridian when it shows an angle of $\mathrm{dip}\theta$ at a place. The dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of $\mathrm{dip}{\theta }^{\prime }$. Then what is the value of $\frac{\tan {\theta }^{\prime }}{\tan \theta }?$

• A. $\frac{1}{\cos x}$
• B. $\frac{1}{\sin x}$
• C. $\frac{1}{\tan x}$
• D. $\cos x$

Answer 1

Answer: (A)

In first case $\tan \theta =\frac{B_V}{B_H}\dots \dots \dots \dots (i)$
In second case, when the needle is rotated at an angle $x$ with the magnetic meridian, the horizontal component of earth's
magnetic field $B_H\cos x$ will be responsible for the orientation of the $\text{dip}$ needle. $\tan {\theta }^{\prime }$
$=\frac{B_V}{B_H\cos x}\dots \dots \dots$ (ii)
Dividing equation (ii) by equation (i)
$\frac{\tan {\theta }^{\prime }}{\tan \theta }=\frac{1}{\cos x}$