Q. 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
Explanation
(a) The horizontal components are $\left( B_{H} \right)_{1} = B\cos\phi_{1}\ $and $\left( B_{H} \right)_{2} = B\cos\phi_{2}$
$\therefore\frac{\left( B_{H} \right)_{1}}{\left( B_{H} \right)_{2}} = \frac{\cos\phi_{1}}{\cos\phi_{2}} = \frac{\cos{30{^\circ}}}{\cos{45{^\circ}}} = \frac{\sqrt{3}}{2}\sqrt{2} = \frac{\sqrt{3}}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.