Question

A dip circle lies initially in the magnetic meridian. If it is now rotated through angle $\theta$ in the horizontal plane, then tangent of the angle of dip is changed in the ratio

• A. $1:\cos \theta$
• B. $\cos \theta :1$
• C. $1:\sin \theta$
• D. $\sin \theta :1$

Answer 1

The correct option is A $1:\cos \theta$

Let V= vertical component of earth’s field ( it remains same in every vertical plane )
H= horizontal component of earth’s field
then horizontal component of field in the plane at angle $\theta$ with magnetic meridian = $H\cos \theta$


Let $\delta and{\delta }^{\prime }$ be the angle of dip in magnetic meridian and another plane at angle $\theta$ with magnetic meridian respectively
in magnetic meridian

$\tan \delta =\frac{V}{H}$
in other plane
$\tan {\delta }^{\prime }=\frac{V}{H\cos \theta }$

$\Rightarrow \frac{\tan \delta }{\tan {\delta }^{\prime }}=\frac{V}{H\cos \theta }\times \frac{H}{V}$

$=\frac{1}{\cos \theta }$

Hence, Correct option is (a)