question_answer

At a certain place, the horizontal component of earth's magnetic field is\[\sqrt{3}\] times of its vertical component, the angle of dip at that. place is :

A) \[75{}^\circ \]                               

B) \[60{}^\circ \]

C) \[45{}^\circ \]                           

D) \[30{}^\circ \]

Correct Answer: D

Solution :

Key Idea: Dip needle becomes vertical at the poles and horizontal at the equator. A dip circle is used to measure the angle between the direction of the earth's magnetic field and the horizontal at any point on the earth's surface. At earth's magnetic poles, the magnetic field of earth is vertical (V) and at  the equator, the field is horizontal (H), hence we have \[\tan \delta =\frac{V}{H}\] Given,    \[H=\sqrt{3}V\] \[\therefore \]     \[\tan \,\,\delta \,=\,\frac{V}{V\sqrt{3}}=\frac{1}{\sqrt{3}}\] \[\delta ={{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)={{30}^{o}}\]