Q.Which of the following is correct for tangent law? (A) B = B_H tanθ
(B) B = B_H^2 tanθ
(C) B = √(B_H) tanθ
(D) B = B_H tan^2 θ

The tangent law states that a magnetic needle, freely suspended in two mutually perpendicular uniform fields, settles along their resultant, at an angle $\theta$ from one field such that

A tangent galvanometer applies this: a compass needle pivoted exactly at the centre of a vertical current-carrying coil experiences the coil's own field $B=\mu_0NI/2R$ acting perpendicular to the Earth's horizontal field $B_H$, and settles at a deflection $\theta$ from which the unknown current can be recovered,

$I = \frac{2R\,B_H}{\mu_0 N}\tan\theta$ …