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Answer the following question regarding earth:
The earth's field, it is claimed, roughly approximates the field due to a dipole of magnetic moment 8 x 10²² J T^–1 located at its centre. Check the order of magnitude of this number in some way.

Solution

Magnetic field B at an equatorial point of the earth's magnetic dipole is given by

B = \frac{μ_{0}}{4 π} . \frac{m}{r^{3}}

Now,

magnetic moment, m = 8 \times 10^{22} {JT}^{- 1} radius, r = 6.4 \times 10^{6} m

Therefore,

B = 10^{- 7} \times \frac{8 \times 10^{22}}{{(6.4 \times 10^{6})}^{3}} T = 0.3 \times 10^{- 4} T = 0.3 G

Which is of the same order of magnitude as that of the observed field on the earth.

Some More Questions From Magnetism and Matter Chapter

Answer the following question:
The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:
The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

A bar magnet of magnetic moment 1.5 JT^–1 lies aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?
(b) What is the torque on the magnet in cases (i) and (ii)?

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