At a certain location in Africa, a compass points 12^{\circ} west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 \mathrm{G} . Specify the direction and magnitude of the earth’s field at the location.At a certain location in Africa, a compass points 12^{\circ} west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 \mathrm{G} . Specify the direction and magnitude of the earth’s field at the location.
At a certain location in Africa, a compass points 12^{\circ} west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 \mathrm{G} . Specify the direction and magnitude of the earth’s field at the location.At a certain location in Africa, a compass points 12^{\circ} west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 \mathrm{G} . Specify the direction and magnitude of the earth’s field at the location.

Ans: In the above question it is given that:
Angle of declination, \theta=12^{\circ}
Angle of dip, \delta=60^{\circ}
Horizontal component of earth’s magnetic field, B_{H}=0.16 \mathrm{G}
Earth’s magnetic field at the given location =\mathrm{B}
We can relate B and B_{H} as:

    \[\begin{array}{l} \mathrm{B}_{\mathrm{H}}=\mathrm{B} \cos \delta \\ \Rightarrow \mathrm{B}=\frac{\mathrm{B}_{\mathrm{H}}}{\cos \delta}=\frac{0.16}{\cos 60^{0}}=0.32 \mathrm{G} \end{array}\]

Earth’s magnetic field lies in the vertical plane, 12^{\circ} West of the geographic meridian, making an angle of 60^{\circ} (upward) with the horizontal direction. Its magnitude is 0.32 \mathrm{G}.