The earth’s magnetic field at the magnetic north pole is directed vertically dow

Question

The earth’s magnetic field at the magnetic north pole is
directed vertically downward and has a magnitude of
0.62 G. The earth’s field is approximately that of a cur -
rent loop located at the center of the earth.
(a) Find the magnitude and direction of the earth’s mag -
netic moment.
(b) It is believed that the earth’s magnetic field is pro -
duced by electric current in the earth’s liquid metallic
outer core. Suppose that the magnetic moment were
produced by a current through a simple circular path
of radius equal to the average radius of the outer
core (2300 km). Find the direction and magnitude of
this current.

Explanation / Answer

a. Magnetic moment m = B * d where B is the strength of magnetic field and d is the diameter of earth. m = 0.62 * 10-4 * 6370 * 103 = 7.90 * 102 A-m2 vertically downwards at north pole. b. Also m = I * A A is area of current loop 7.90 * 102 = I * p * (2300 * 103)2 Current I = 7.90 * 102 / 3.14 * 2.37 * 10 = 4.74 * 10-11 A By right hand thumb rule, direction of current is clockwise as seen from north pole.

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