A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 30° with the horizontal. The horizontal component of the earth's magnetic field at the place is B. The strength of the earth's magnetic field at the place is:

$\frac{2 B}{\sqrt{3}}$

The correct answer is Option (1) → $\frac{2 B}{\sqrt{3}}$

The angle of dip ($δ$) is the angle between the earth's magnetic field and the horizontal $B_H$

$B_H=B_E\cos δ$

$B_E=\frac{B_H}{\cos δ}$

$δ=30°$ [given]

$B_H=B$ [given]

$∴B_E=\frac{B}{\cos 30}=\frac{2 B}{\sqrt{3}}$