The line on the earth's surface joining the points where the field is horizontal is

A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of $30$ turns and radius $12 \;cm .$ The coil is in a vertical plane making an angle of $45^{\circ}$ with the magnetic meridian. When the current in the coil is $0.35 \;A$, the needle points west to east.

$(a)$ Determine the horizontal component of the earth's magnetic field at the location.

$(b)$ The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of $90^{\circ}$ in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.

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 $ \pm $ $45^{°}$

What was the recognition of Earth’s magnetic field ? State dynamo effect

The earth's magnetic field was flipped by $180^{\circ}$ a million years ago. This flip was relatively rapid and took $10^5 \,yrs$. Then, the average change in orientation per year during the flip was closest to ............ $s$

Earth's magnetic field always has a horizontal component except at or Horizontal component of earth's magnetic field remains zero at