Question

At two different places the angles of dip are respectively ${30}^0$ and ${45}^0$. At these two places the ratio of horizontal component of earths magnetic field is

• A. $\sqrt{3}:\sqrt{2}$
• B. $1:\sqrt{2}$
• C. $1:2$
• D. $1:\sqrt{5}$

Answer 1

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

Horizontal component of earth's magnetic field $B_H=B\cos \delta$ where $B$ is earth's magnetic field

$⟹$ $\frac{B_H}{B_H^{\prime }}=\frac{\cos \delta }{\cos {\delta }^{\prime }}$

Given : $\delta ={30}^o$ $\cos {\delta }^{\prime }={45}^o$

$\therefore$ $\frac{B_H}{B_H^{\prime }}=\frac{\cos {30}^o}{\cos {45}^o}=\frac{\sqrt{3}/2}{1/\sqrt{2}}$

$⟹$ $B_H:B_H^{\prime }=\sqrt{3}:\sqrt{2}$