The magnetic field of the Earth at the equator is approximately $4 \times 10^{-5} \, T$. The radius of the Earth is $6.4 \times 10^6 \, m$. Then the dipole moment of the Earth will be nearly of the order of:

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

$A$ compass needle will show which one of the following directions at the Earth's magnetic pole?

$A$ magnet is suspended in such a way that it oscillates in the horizontal plane. It makes $20$ oscillations per minute at a place where the dip angle is $30^{\circ}$ and $15$ oscillations per minute at a place where the dip angle is $60^{\circ}$. The ratio of the total Earth's magnetic field at the two places is:

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.

If the magnetic declination at a place is known to be $15^{\circ} \, E$,and a compass needle points as shown in the figure,then the geographic north is represented by which numbered direction?