The angles of dip at two places are `30^(@)` and `45^(@)` respectively . What is the ratio of horizontal components of earth's magnetic field at the two planes , if vertical components at the two places are same ?

Explanation

As we know , `tan phi = (B_(V))/(B_(H))`
`implies B_(V) = B_(H) tan phi`
Now , at the two vertical places , `B_(V)` are same . So , we have
`B_(H) tan phi = B_(H) tan phi `
`(B_(H))/(B_(H')) = (tan phi')/(tan phi) = (tan 45^(@))/(tan 30^(@)) = sqrt3`