The horizontal component of Earth's magnetic field at a place is $3.5 \times 10^{-5} \,T$. $A$ very long straight conductor carrying a current of $\sqrt{2} \,A$ in the direction from South-East to North-West is placed. The force per unit length experienced by the conductor is $..............$ $\times 10^{-6} \,N/m$.

The total intensity of the Earth's magnetic field at the magnetic equator is $5$ $units$. Its value at a magnetic latitude of $37^{\circ}$ is equal to:

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:

If the angle of dip at places $A$ and $B$ are $30^{\circ}$ and $45^{\circ}$ respectively,the ratio of the horizontal component of the Earth's magnetic field at $A$ to that at $B$ will be.
$[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}, \quad \sin 30^{\circ}=\frac{1}{2}, \quad \cos 30^{\circ}=\frac{\sqrt{3}}{2}]$

$A$ magnetic needle is free to rotate in a vertical plane which makes an angle of $60^{\circ}$ with the magnetic meridian. If the needle stays in a direction making an angle of $\tan^{-1}\left(\frac{2}{\sqrt{3}}\right)$ with the horizontal,the true dip value at that place is: (in $^{\circ}$)

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?