Let $V$ and $H$ be the vertical and horizontal components of the Earth's magnetic field at any point on Earth. Near the North Pole:

Planets producing larger magnetic field have larger

The angle of dip at a place is $60^{\circ}$. At this place,the total intensity of the Earth's magnetic field is $0.64 \text{ units}$. The horizontal intensity of the Earth's magnetic field at this place is . . . . . . $\text{units}$.

At a certain place,the angle of dip is $30^{\circ}$ and the horizontal component of the Earth's magnetic field is $0.50 \text{ Oersted}$. The Earth's total magnetic field is:

At a certain place,the horizontal component of the Earth's magnetic field is $B_0$ and the angle of dip is $45^o$. The total intensity of the Earth's magnetic field at that place will be:

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?