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 $60^{\circ}$ 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.
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 $60^{\circ}$ 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.
Angle of declination, $\theta=12^{\circ}$
Angle of dip, $\delta=60^{\circ}$
Horizontal component of earth's magnetic field, $B_{H}=0.16 \,G$
Earth's magnetic field at the given location $=B$
We can relate $B$ and $B_{H}$ as:
$B_{H}=B \cos \delta$
$\therefore B=\frac{B_{H}}{\cos \delta}$
$=\frac{0.16}{\cos 60^{\circ}}=0.32 \,G$
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 $0.32\, G.$
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