Question

The angles of dip at the poles and the equator respectively are:
A.)$30^{\circ} , 60^{\circ}$
B.)$0^{\circ} , 90^{\circ}$
C.)$45^{\circ} , 90^{\circ}$
D.)$90^{\circ} , 0^{\circ}$

Answer 1

Hint: Angle of dip or the magnetic dip or magnetic inclination is the angle made by the earth’s magnetic field and the plane of horizon at any given location. Since earth’s magnetic field $B$ is a vector quantity, it has two components: Horizontal component and Vertical component.

Complete solution Step-by-Step: Angle of dip or the magnetic dip or magnetic inclination is the angle made by the earth’s magnetic field and the plane of horizon at any given location. Clearly this value varies at different places on the surface of the earth.
Since earth’s magnetic field $B$ is a vector quantity, it has two components:

Horizontal component of earth’s magnetic field $B$ : $B_{H} =B\cos\theta$
Vertical component of earth’s magnetic field $B$: $B_{V} =B\sin\theta$

At the poles, the earth’s magnetic field is perpendicular to the surface of the earth, or the horizontal component of the earth’s magnetic field is zero. $B$ ie) $B_{H} =B\cos\theta =0$. Hence, a freely suspended bar magnet, will align itself vertically.

Similarly, at the magnetic equator, the earth’s magnetic field is parallel to the surface of the earth, or the vertical component of the earth’s magnetic field is zero. $B$ ie) $B_{V} =B\sin\theta =0$.Hence,a freely suspended bar magnet, will align itself horizontally.

 Thus, the answer is D. It varies from 90⁰ to 0⁰ from the poles to the equator.

Note:
Angle of dip or the magnetic dip or magnetic inclination is the angle made by the earth’s magnetic field and the plane of horizon at any given location. It is generally used for measuring and correcting the magnetic compass error. It is also used in geological field mapping. For a tilted plank the angle of dip helps in determining the steepest angle of descent with respect to the horizontal plane. Angle of dip is of importance in the field of aviation as it causes the airplane to give error in reading during the speed change and turnings.