At a certain location in Africa, a compass points 12° west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60° 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.

Answer –

We are given the angle of declination, θ = 12°

Angle of dip, given by δ = 60°

Horizontal component of earth’s magnetic field is given by B_H = 0.16 G

Earth’s magnetic field at the given location is = B

We can relate B and B_H in following manner –

${{B}_{H}}=B\cos \delta $

Rearranging the above relation, we get –

$B=\frac{{{B}_{H}}}{\cos \delta }=\frac{0.16}{\cos {{60}^{\circ }}}$$$

$B=0.32G$

The magnetic field of the Earth is located in the vertical plane, 12 degrees west of the geographic meridian, and forms a 60-degree (upward) angle with the horizontal direction. It is 0.32 G in magnitude.