Question

If the angles of dip at two different places are ${30}^{\circ }$ and ${45}^{\circ }$ respectively, then the ratio of horizontal components of earth's magnetic field at the two places will be

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

Answer 1

The correct option is A $\sqrt{\frac{3}{2}}$

If $\varphi$ is the angle of dip, then the horizontal and the vertical component of the earth's magnetic field is given by,

$B_H=B\cos \varphi$

$B_V=B\sin \varphi$

As per the question, if $B_{H_1}$ and $B_{H_2}$ are the horizontal component of earth's magnetic field at two different places.

Then,

$B_{H_1}=B\cos {30}^{\circ }$, and

$B_{H_2}=B\cos {45}^{\circ }$

$\therefore \frac{B_{H_1}}{B_{H_2}}=\frac{\cos {30}^{\circ }}{\cos {45}^{\circ }}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}}}$

$\Rightarrow \frac{B_{H_1}}{B_{H_2}}=\sqrt{\frac{3}{2}}$

Hence, option $\left(A\right)$ is the correct answer.