Assume the dipole model for earth’s magnetic field $\mathrm{B}$ which is given by

${{\rm{B}}_{\rm{v}}} = $ vertical component of magnetic field

$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{2m\,\cos \theta }}{{{r^3}}}$

${{\rm{B}}_H} = $ Horizontal component of magnetic field

${{\rm{B}}_H} = \frac{{{\mu _0}}}{{4\pi }}\frac{{m\,\sin \theta }}{{{r^3}}}$

$\theta $ $= 90^{°}$ -latitude as measured from magnetic equator.

$(a)$ Find loci of points for which : dip angle is zero;

Angle of dip is $90^o$ at

If $\theta _1$ and $\theta_2$ be 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 

At a point $A$ on the earth's surface the angle of $\operatorname{dip}, \delta=+25^{\circ} .$ At a point $B$ on the earth's surface the angle of dip, $\delta=-25^{\circ} .$ We can interpret that

Intensity of magnetic field due to earth at a point inside a hollow steel box is

The horizontal component of the earth's magnetic field at any place is $0.36 \times 10^{-4} Wb / m ^{2}$. If the angle of dip at that place is $60^{\circ}$, then the value of vertical component of the earth's magnetic field will be ........ $\times 10^{-4}\;W b / m^{2}$