Question

If the angle of dip at places A and Bare 30° and 45° respectively, then the ratio of horizontal component of earth's magnetic field at A to that at B will be
`[sin 45^circ = cos 45^circ = 1/sqrt2, sin  pi/6 = 1/2, cos  pi/6 = sqrt3/2]`

विकल्प

• `sqrt2 : 1`

• `1 : sqrt2`

• `sqrt3 : sqrt2`

• `sqrt2 : sqrt3`

Answer 1

`sqrt3 : sqrt2`

Explanation:

The horizontal component of earth's magnetic field,

H = B cos δ

At place A, 

H_A = B cos δ_A

= B cos 30° = `(sqrt3"B")/2`

At place B,

H_B = B cos δ_B

= B cos 45°

= `"B"/sqrt2`

The ratio of H_A : H_B becomes,

`"H"_"A"/"H"_"B" = (sqrt3"B")/2 xx sqrt2/"B" = sqrt3/sqrt2`