The magnetic dip angle at two places are 30° and 45°. Calculate ratio of horizontal components of earth's magnetic field at the two places. Magnetic field at the places is equal to .......

Options

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

Answer

B

Explanation

If `phi` is dip angle then horizontal component
`B_h = B cos phi`
Taking ratio of `B_(h_(1) ) = B cos phi_(1)and B_(h_(2) ) = B cos phi_(2) `
`therefore (B_(h_(1) ) )/( B_(h_(2) ) ) = ( cos phi_(1) )/( cos phi_(2 )) " "[phi_(1) = 30^(@) , phi_(2) = 45^(@) ]`
`= ( cos 30^(@) )/( cos 45^(@) ) `
`= ( sqrt3//2)/( 1//2) = (sqrt(3)xxsqrt(2) )/( 2 ) = (sqrt(3) )/( sqrt(2))`