A magnetic needle free to rotate about the vertical direction (compass ) point `3.5` west of the geographic north . Another magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at `18^(@)` with the horizontal . The magnitude of the horizontal component of the earth ' magnetic field at the place is known to be `0.40 G` . what is the direction and magnitude of the earth's magnetic field at the place ?

Explanation

`B_(H) = B_(e) cos delta`
`0.40 = B_(e) cos 18^(@)`
`0.40 = B_(e) xx 0.95`
`B_(e) = (0.40)/(0.95) G`
`B_(e) = 0.42 `G