The magnetic compass is not useful for navigation near the magnetic poles because

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 zero.

$A$ dip needle lies initially in the magnetic meridian when it shows an angle of dip $\theta$ at a place. The dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of dip $\theta'$. Then $\frac{\tan \theta'}{\tan \theta}$ is

The direction of the null points is on the equatorial line of a bar magnet,when the north pole of the magnet is pointing

If a magnet is suspended freely such that it can rotate about its magnetic axis,in which plane does it come to rest?

The total intensity of the Earth's magnetic field at the magnetic equator is $5$ $units$. Its value at a magnetic latitude of $37^{\circ}$ is equal to: