At a place the angle of dip is 30°. If the horizontal component of the earth's magnetic field is $B_{H}$, the total magnetic field of the earth will be:

$2 B_{H} / \sqrt{3}$

The correct answer is Option (2) → $2 B_{H} / \sqrt{3}$

$\tan θ=\frac{B_V}{B_H}$ [formula]

where,

$\tan θ$, θ = Angle of Dip

$B_V$ = Vertical component of earth magnetic field

$B_H$ = Horizontal component of earth magnetic field

$B=\sqrt{B_H^2+B_V^2}$

where,

B = total magnetic field

and,

$B_V=B_H\tan θ$

$B=\sqrt{B_H^2+(B_H\tan θ)^2}$

$=B_H\sqrt{1+\tan^2θ}$

$=B_H\sec θ$

$=B_H\sec 30°$

$=B_H\frac{2}{\sqrt{3}}$