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. $1:2$
• D. $1:\sqrt{3}$

Answer 1

The correct option is B $1:\sqrt{2}$

The horizontal component of earth's magnetic field is given by , $H=R\cos \delta$
where, $\delta$ is the angle of dip so $H_1=R\cos {30}^o$
and $H_2=R\cos {45}^o$
$\therefore \frac{H_1}{H_2}=\frac{R\cos {30}^o}{R\cos {45}^o}=\frac{\sqrt{3}/2}{1/\sqrt{2}}=\frac{\sqrt{3}}{\sqrt{2}}$