Question

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 $0.16\text{G}.$ What is the direction and magnitude of the Earth's field at the location?

• A. ${12}^{\circ }$west of the geographic meridian and $0.32\text{G}$.
• B. ${12}^{\circ }$ east of the geographic meridian and $0.32\text{G}$.
• C. ${72}^{\circ }$ west of the geographic meridian and $0.32\text{G}$.
• D. ${72}^{\circ }$ east of the geographic meridian and $0.32\text{G}$.

Answer 1

The correct option is A ${12}^{\circ }$west of the geographic meridian and $0.32\text{G}$.

Given, Angle of declination, $\theta ={12}^{\circ }$

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

Horizontal component of earth's magnetic field, $B_H=0.16\text{G}$

Let earth's magnetic field at the given location be $B$

Hence, we can relate $B\text{and}{B}_H$ as,

$B_H=B\cos \delta$

$\therefore B=\frac{B_H}{\cos \delta }$

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

Earths 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.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.

Key concept: Angle of dip $\left(\delta \right)$: is the angle between horizontal component of the earth's magnetic field to the total magnetic field of earth's magnetic field.