Dip angle in vertical plane at an angle ${\cos ^{ - 1}}\,\left( {\frac{1}{{\sqrt 2 }}} \right)$ from magnetic meridian is $60^o$, then actual dip at that place

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;

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 $0.16 \;G$. Specify the direction and magnitude of the earth's field at the location.

The value of horizontal component of earth's magnetic field at a place is $0.35 \times 10^{-4} \,T$. If the angle of dip is $60^{\circ}$, the value of vertical component of earth's magnetic field is nearly ............. $\times 10^{-4} \,T$

A line passing through places having zero value of magnetic dip is called

The vertical component of earth's magnetic field is zero at or The earth's magnetic field always has a vertical component except at the