The pole near the geographic north pole is called ...... . The pole near the geographic south pole is called ...... .

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;

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at $22^o$ with the horizontal. The horizontal component of the earth’s magnetic field at the place is known to be $0.35\; G$. Determine the magnitude of the earth’s magnetic field (in $G$) at the place

A compass needle of oscillation magnetometer oscillates $20$ times per minute at a place $P$ of dip $30^{\circ}$. The number of oscillations per minute become $10$ at another place $Q$ of $60^{\circ} dip$. The ratio of the total magnetic field at the two places $\left(B_{Q}: B_{p}\right)$ is.

At a certain place, the horizontal component of earth's magnetic field is $\sqrt 3 $times the vertical component. The angle of dip at that place is....$^o$

Give information about Earth’s magnetism.