(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°. 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, is 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 the magnetic moment 8 × 1022 JT-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 :
(a) Following are the three independent conventional quantities which are used for determining the earth’s magnetic field:
(i) Magnetic declination,
(ii) Angle of dip
(iii) The horizontal component of the earth’s magnetic field
(b) The angle of dip at a point is determined by the distance between the North Pole and the South Pole. As a result, because Britain lies closer to the magnetic North Pole on the globe, the angle of dip in Britain (about 70°) is greater than in southern India.
(c) A massive bar magnet is thought to be submerged within the globe, with its north pole near the geographic South Pole and its south pole near the geographic North Pole.
Magnetic field lines extend from the magnetic north pole to the magnetic south pole. As a result, the field lines at Melbourne, Australia appear to travel away from the ground on a map depicting the earth’s magnetic field lines.
(d) A compass placed in the geomagnetic North Pole or South Pole will be free to move in the horizontal plane while the earth’s field is perfectly vertical to the magnetic poles. The compass in this scenario can point in any direction.
(e) Magnetic moment is given by
\[M=8\times {{10}^{22}}J{{T}^{-1}}\]
Radius of earth is given by –
\[r=6.4\times {{10}^{6}}m\]
Magnetic field strength is given by the relation-
\[B=\frac{{{\mu }_{0}}M}{4\pi {{r}^{3}}}\]
Where \[{{\mu }_{0}}=4\pi \times {{10}^{-7}}Tm{{A}^{-1}}\]
\[\therefore B=\frac{4\pi \times {{10}^{-7}}\times 8\times {{10}^{22}}}{4\pi {{\left( 6.4\times {{10}^{6}} \right)}^{3}}}=0.3G\]
This quantity is of the order of magnitude of the observed field on earth.
(f) Yes, there are several local poles which are oriented in different directions on earth’s surface . An example of which would be magnetized mineral deposit of a local N-S pole.