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:

The relations among the three elements of Earth's magnetic field,namely horizontal component $H$,vertical component $V$,and angle of dip $\delta$ are,($B_{E} =$ total magnetic field):

At a certain location in Africa,a compass points $12^{\circ}$ West of the geographic North. The North tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points $60^{\circ}$ above the horizontal. The horizontal component of the earth's field is measured to be $0.16\, G$. The magnitude of the earth's field at the location will be

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 $|\vec{B}|$ is minimum.

At a place,the horizontal and vertical intensities of the Earth's magnetic field are $0.30 \ G$ and $0.173 \ G$ respectively. The angle of dip at this place is.....$^o$

If $\theta_1$ and $\theta_2$ are the apparent angles of dip observed in two vertical planes at right angles to each other,then the true angle of dip $\theta$ is given by: