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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.
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Given: Angle of dip $\delta=60^{\circ}$; Horizontal component of earth's magnetic field $\mathrm{H}=0.16 \mathrm{G}$
To find: Earth's magnetic field $=\mathrm{B}$
Formula used: $\mathrm{H}=\mathrm{B} \cos \delta$
$$
\begin{aligned}
&\mathrm{H}=\mathrm{B} \cos \delta \\
&\Rightarrow \mathrm{B}=\frac{\mathrm{H}}{\cos \delta}=\frac{0.16}{\cos 60^{\circ}}=\frac{0.16}{0.5}=0.32 \mathrm{G}
\end{aligned}
$$
The magnetic field of the earth lies $12^{\circ}$ West of the geographic meridian (of Africa) at an angle of $60^{\circ}$ (upwards) with respect to the horizontal.
To find: Earth's magnetic field $=\mathrm{B}$
Formula used: $\mathrm{H}=\mathrm{B} \cos \delta$
$$
\begin{aligned}
&\mathrm{H}=\mathrm{B} \cos \delta \\
&\Rightarrow \mathrm{B}=\frac{\mathrm{H}}{\cos \delta}=\frac{0.16}{\cos 60^{\circ}}=\frac{0.16}{0.5}=0.32 \mathrm{G}
\end{aligned}
$$
The magnetic field of the earth lies $12^{\circ}$ West of the geographic meridian (of Africa) at an angle of $60^{\circ}$ (upwards) with respect to the horizontal.
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