Assertion: If a compass needle is kept at the magnetic north pole of the Earth,the compass needle may stay in any direction.
Reason: $A$ dip needle will stay vertical at the north pole of the Earth.

$A$ long vertical wire carries a steady current of $5.0 \, A$. $A$ sensitive magnetic compass is placed in a plane perpendicular to the wire and $10.0 \, cm$ south of it. It registers a deflection of $60^{\circ}$ north of east. The magnitude of the horizontal component of the earth's magnetic field is (permeability of free space is $4 \pi \times 10^{-7} \, N/A^2$):

If the angles of dip at two places are $30^{\circ}$ and $45^{\circ}$ respectively,then the ratio of horizontal components of earth's magnetic field at the two places will be

The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to $8 \times 10^{22} \text{ Am}^2$,the value of earth's magnetic field near the equator is close to $.... \text{ Gauss}$ (radius of the earth $= 6.4 \times 10^6 \text{ m}$)

The lines joining the places of the same horizontal intensity are known as

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?