# At a certain location in Africa, a compass points 12º west of the geographic north.

Question:

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.

Solution:

Angle of declination,θ = 12°

Angle of dip, $\delta=60^{\circ}$

Horizontal component of earth’s magnetic field, BH = 0.16 G

Earth’s magnetic field at the given location = B

We can relate and BHas:

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

$\therefore B=\frac{B_{H}}{\cos \delta}$

$=\frac{0.16}{\cos 60^{\circ}}=0.32 \mathrm{G}$

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