Question

Question 5.11: At a certain location in Africa, a compass points 12º west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60º above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 G. Specify the direction and magnitude of the earth’s field at the location.

Class 12 - Physics - Magnetism And Matter Magnetism And Matter Page-201

Answer 1

compass needle points 12° west of geographical north, hence angle of declination $\theta$ is 12° west.
north tip of magnitude needle is 60° above horizontal, hence the location is in southern hemisphere and angle of dip is 60°.

magnitude of net magnetic field can be calculated as $\bf{B=\frac{B_H}{cos\delta}}$
here, $B_H$=0.16G and $\delta$=60°
so, B = 0.16G/cos60° = 0.32G