Question

If the angles of dip at two 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. $\sqrt{3}:\sqrt{2}$
• B. $1:\sqrt{2}$
• C. $1:\sqrt{3}$
• D. $1:2$

Answer 1

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


We know that,

$\cos \delta =\frac{B_H}{B}$

$\Rightarrow B_H=B\cos \delta$

$\therefore \frac{(B_H{)}_1}{(B_H{)}_2}=\frac{\cos {\delta }_1}{\cos {\delta }_2}=\frac{\cos {30}^{\circ }}{\cos {45}^{\circ }}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}}}$

$\frac{(B_H{)}_1}{(B_H{)}_2}=\frac{\sqrt{3}}{\sqrt{2}}$

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