At some location on Earth,the horizontal component of Earth's magnetic field is $18 \times 10^{-6} \ T$. At this location,a magnetic needle of length $0.12 \ m$ and pole strength $1.8 \ A \ m$ is suspended from its mid-point using a thread. It makes a $45^{\circ}$ angle with the horizontal in equilibrium. To keep this needle horizontal,the vertical force that should be applied at one of its ends is:

At a point $A$ on the earth's surface, the angle of dip is $\delta = +25^{\circ}$. At a point $B$ on the earth's surface, the angle of dip is $\delta = -25^{\circ}$. We can interpret that:

If ${\phi_1}$ and ${\phi_2}$ are the angles of dip observed in two vertical planes at right angles to each other and ${\phi}$ is the true angle of dip,then:

The horizontal component of the Earth's magnetic field is $0.22 \ G$ and the total magnetic field is $0.4 \ G$. The angle of dip 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?

At two different places,the angles of dip are respectively $30^{\circ}$ and $45^{\circ}$. At these two places,the ratio of the horizontal component of Earth's magnetic field is: