If the angle of dip at two places are `30^(@)` and `45^(@)` respectively, then the ratio of horizontal components of earth's magnetic field at the two places will be

Options

A. `sqrt(3):sqrt(2)`
B. `1:sqrt(2)`
C. `1:sqrt(3)`
D. `1:2`

Answer

A

Explanation

The horizontal componenets are `(B_(H))_(1)=B cos varphi_(1)` and
`(B_(H))_(2)= B cos varphi_(2)`
`:. (B_(H))_(1)/(B_(H))_(2)=(cos varphi_(1))/(cos varphi_(2))=(cos 30^(@))/(cos 45^(@))=sqrt(3)/2xxsqrt(2)=sqrt(3)/sqrt(2)`