A magnetic needle is free to rotate in a vertical plans parallel to the magnetic meridian has its north tip down at `60^(@)` with horizontal . The horizontal component of the earth's magnetic field at the place is known to be `0.4 xx 10^(-4)` T determine the magnitude of earth's magnetic field at the place.

Explanation

Angle of dip `theta = 60^(@)`
`H = 0.4 xx 10^(-4) T`
If `B_(e)` is the earth's magnetic field , then
`H = B_(e) cos theta`
` B_(e) = H/(cos theta) = (0.4 xx 10^(-4)T)/(cos 60^(@))`
` = 0.8 xx 10^(-14)` T