The correct value of dip angle at a place is `45^(@)`. If the dip circle is rotated by `45^(@)` out of the meridian, then the tangent of the angle of apparent dip at the place is

Answer

2

Explanation

Let `B_V` and `B_H` are vertical and horizontal components of magnetic field due to earth. If `delta` is actual angle of dip then we can write the following:
` tan delta = (B_V)/(B_H)`
` rArr tan 45^@ = (B_V)/(B_H)`
`rArr 1 = (B_V)/(B_H)`
` rArr B_V = B_H` ....(i)
When dip circle is rotated by an angle `45^@` from magnetic meridian then needle gets aligned along the resultant of `B_V` and `B_H cos 45^@` , hence apparent dip can be written as follows:
` tan delta. = (B_V)/(B_H cos 45^@)` Using equation (1) we get the following:
`tan delta. = sqrt2`
` tan^2 delta. = 2`