A magnetic needle free to rotate in a vertical plane

Horizontal component of earth’s magnetic field, BH = 0.35 G

Angle made by the needle with the horizontal plane $=$ Angle of dip $=\delta=22^{\circ}$

Earth’s magnetic field strength = B

We can relate B and BHas:

$B_{H}=B \cos \theta$

$\therefore B=\frac{B_{H}}{\cos \delta}$

$=\frac{0.35}{\cos 22^{\circ}}=0.377 \mathrm{G}$

Hence, the strength of earth’s magnetic field at the given location is 0.377 G.