$A$ magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at $22^{\circ}$ with the horizontal. The horizontal component of the earth's magnetic field at the place is known to be $0.35 \; G$. Determine the magnitude of the earth's magnetic field (in $G$) at the place.

Choose the correct option regarding the relationship between true dip $(\phi)$ and apparent dip $(\phi^{\prime})$:

Assume the dipole model for Earth's magnetic field $B$,which is given by:
$B_v = \text{vertical component of magnetic field} = \frac{\mu_0}{4\pi} \frac{2m \cos \theta}{r^3}$
$B_H = \text{horizontal component of magnetic field} = \frac{\mu_0}{4\pi} \frac{m \sin \theta}{r^3}$
where $\theta = 90^{\circ} - \text{latitude}$ as measured from the magnetic equator.
$(a)$ Find the loci of points for which the dip angle is $\pm 45^{\circ}$.

Give the location of magnetic:
$(i)$ north pole
$(ii)$ south pole

At a certain place, the angle of dip is $60^{\circ}$ and the horizontal component of the earth's magnetic field $(B_H)$ is $0.8 \times 10^{-4} \,T$. The earth's overall magnetic field is

$A$ dip circle is at a right angle to the magnetic meridian. What will be the apparent dip in degrees?