# 11. At a certain location in Africa, a compass points $12 \degree$ west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points $60 \degree$ 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.

Given,

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

The angle of declination, $\theta$ = $12^{\circ}$

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

We know, $\dpi{100} B_{H}$ = B cos$\delta$, where B is Earth's magnetic field

B = $\dpi{100} B_{H}$/cos$\delta$ = 0.16/(cos$60 \degree$) = 0.32 G

Earth’s magnetic field is 0.32 G in magnitude lying in the vertical plane, $12^{\circ}$ west of the geographic meridian and $60^{\circ}$ above the horizontal.

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