Assertion : In high latitudes,one sees colourful curtains of light hanging down from high altitudes.
Reason : The high-energy charged particles from the sun are deflected to polar regions by the magnetic field of the earth.

Answer the following questions regarding earth's magnetism:
$(a)$ $A$ vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth's magnetic field.
$(b)$ The angle of dip at a location in southern India is about $18^o$. Would you expect a greater or smaller dip angle in Britain?
$(c)$ If you made a map of magnetic field lines at Melbourne in Australia,would the lines seem to go into the ground or come out of the ground?
$(d)$ In which direction would a compass free to move in the vertical plane point to,if located right on the geomagnetic north or south pole?
$(e)$ The earth's field,it is claimed,roughly approximates the field due to a dipole of magnetic moment $8 \times 10^{22} \, J \, T^{-1}$ located at its centre. Check the order of magnitude of this number in some way.
$(f)$ Geologists claim that besides the main magnetic $N-S$ poles,there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

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 the dip angle is $\pm 45^{\circ}$.

Two bar magnets with magnetic moments $2M$ and $M$ are fastened together at right angles to each other at their centres to form a crossed system,which can rotate freely about a vertical axis through the centre. The crossed system sets in the Earth's magnetic field with the magnet having magnetic moment $2M$ making an angle $\theta$ with the magnetic meridian such that:

In India,the magnetic declination at Delhi is . . . . . . .

$A$ magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at $30^{\circ}$ with the horizontal. The horizontal component of the earth's magnetic field at the place is $0.3 \ G$. Then the magnitude of the earth's magnetic field at the location is