$A$ dip circle is adjusted so that its needle moves freely in the magnetic meridian. In this position,the angle of dip is $40^{\circ}$. Now the dip circle is rotated so that the plane in which the needle moves makes an angle of $30^{\circ}$ with the magnetic meridian. In this position,the needle will dip by an angle:

The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to $8 \times 10^{22} \text{ Am}^2$,the value of earth's magnetic field near the equator is close to $.... \text{ Gauss}$ (radius of the earth $= 6.4 \times 10^6 \text{ m}$)

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.

The correct relation is:
$B_H$ = Horizontal component of earth's magnetic field; $B_V$ = Vertical component of earth's magnetic field and $B$ = Total intensity of earth's magnetic field.

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

Let $V$ and $H$ be the vertical and horizontal components of the Earth's magnetic field at any point on Earth. Near the North Pole: