Let $m$ and $r$ be the dipole moment and radius of the Earth, respectively. Then, the Earth's magnetic field at the equator is

At a place,if the earth's horizontal and vertical components of magnetic fields are equal,then the angle of dip will be.......$^o$

If a magnet is suspended at an angle $30^o$ to the magnetic meridian,it makes an angle of $45^o$ with the horizontal. The real dip is

$A$ magnetic compass needle oscillates $30$ times per minute at a place where the angle of dip is $45^{\circ}$, and $40$ times per minute at a place where the angle of dip is $30^{\circ}$. If $B_1$ and $B_2$ are respectively the total magnetic field due to the earth at the two places, then the ratio $B_1/B_2$ is best given by:

$A$ 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

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?