Question

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?

Answer 1

(a) The three quantities are:-
1. Magnetic declination
2.Angle of dip and
3. The horizontal component of the earth's magnetic field.
(b) Britain is close to magnetic north pole. Therefore, the angle of dip is grater in Britain than in India. It is about ${70}^o.$
(c) The magnetic field lines of the earth could seem out of the ground. It is because, Melbourne (Australia) is in Southern hemisphere.
(d) The magnetic compass needle can point in any direction on the geomagnetic north or South pole. It is because the horizontal component of the earth's field is zero at these points
($\because$ The earth's field is vertical).
(e) The magnetic field at a point on the equatorial line of the ,agnetic dipole (earth as a magnetic dipole) is given by,
$B=\frac{{\mu }_0}{4\pi }\times \frac{M}{r^3}$
$M=8\times {10}^{22}J{Y}^{-1}$
$r=6.4\times {10}^{6}m$
$\therefore B={10}^{-7}\times \frac{8\times {10}^{22}}{(6.4\times {10}^6{)}^3}=0.3\times {10}^{-4}T=0.3G$
It is really of the order of the observed field of earth
(f) The earth's magnetic field is only approximately a dipole field. The local $N>S$ poles may be oriented due to the different deposits of magnetised minerals.