Question

A dip circle is kept in such a way that its plane makes an angle of ${30}^{\circ }$ with the magnetic meridian. The measured value of the angle of dip is ${45}^{\circ }$. What will be its true value at that place?

• A. ${\tan }^{-1}\frac{1}{2}$
• B. ${\tan }^{-1}1$
• C. ${\tan }^{-1}\frac{\sqrt{3}}{2}$
• D. ${\tan }^{-1}\sqrt{3}$

Answer 1

The correct option is C ${\tan }^{-1}\frac{\sqrt{3}}{2}$

Let the vertical component and horizontal component of earth's magnetic field along magnetic meridian be $V$ and $H$ respectively.
Angle of dip: $\tan \theta =\frac{V}{H}$ ...(1)

If plane of the dip circle make ${30}^{\circ }$ with the magnetic meridian, angle of dip is ${45}^{\circ }$ below horizontal.
$\tan {45}^{\circ }=\frac{V}{H\cos {30}^{\circ }}=1$
$\Rightarrow \frac{V}{H}=\cos {30}^{\circ }$ ...(2)
Comparing (1) and (2),
$\tan \theta =\cos {30}^{\circ }$
or $\theta ={\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$