At a certain location in Africa, compass points `12^@` west of geographic north, figure. The north tip of magnetic needle of a dip circle placed in the plane of magnetic meridian points `60^@` above the horizontal. The horizontal component of earth's field is measured to be `0.16 gauss`. Specify the direction and magnitude of the earth's field at the location.

Explanation

Angle of declination `theta=12^(@)`
Angle of dip, `delta=60^(@)`
Horizontal componen t of earth's magnetic field `B_(H)=0.16G`
Earth's magnet field at the given location=B
We can relate B and `B_(H)` as:
`B_(H)=Bcos delta`
`thereforeB=(B_(H))/(cos delta)`
`=(0.16)/(cos 60^(@))=0.32G`
Earths magnetic field lies in the vertical plan e. `12^(@)` west of the geographic meridian, making an angle of `60^(@)` (upward) with the horizontal direction. its magnitude is 0.32G.