Question

At a certain location in Africa, a compass point ${12}^{\circ }$ 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 $0.16G$. Specify the direction and magnitude of the earth’s field at the location.

Answer 1

Horizontal component of the earth’s magnetic field,$B_H=0.16G$

Angle made by the needle with the horizontal plane = angle of dip, $\delta ={60}^{\circ }$

Now, if $B$ is the earth’s magnetic field at that point, then

$B_H=B\cos \delta \Rightarrow B=\frac{B_H}{\cos \delta }\Rightarrow B=\frac{0.16}{\cos {60}^{\circ }}$

$B=\frac{0.16}{0.5}=0.32G$

Final Answer: The earth’s magnetic field is $0.32G$ and it lies in the vertical plane, ${12}^{\circ }$ west of the geographic meridian, making an angle ${60}^{\circ }$ (upward) with the horizontal direction.