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  4. A short bar magnet is arranged with its North pole pointing geographical North. It is found that the horizontal component of Earths magnetic induction (BH ) is balanced by the magnetic induction of the magnet at a point which is at a distance of 20 cm from its centre. The magnetic moment of the magnet is (if BH=4× 10-5Wb text -m-2 )

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Q. A short bar magnet is arranged with its North pole pointing geographical North. It is found that the horizontal component of Earths magnetic induction (BH ) is balanced by the magnetic induction of the magnet at a point which is at a distance of 20 cm from its centre. The magnetic moment of the magnet is (if $ {{B}_{H}}=4\times {{10}^{-5}}Wb\text{ }-{{m}^{-2}} $ )

EAMCETEAMCET 2010Magnetism and Matter

Solution:

$ {{B}_{H}}=\frac{{{\mu }_{0}}}{4\pi }.\frac{M}{{{r}^{3}}} $ $ 4\times {{10}^{-5}}={{10}^{-7}}\times \frac{M}{{{(20)}^{3}}{{10}^{-6}}} $ $ \frac{{{(20)}^{3}}\times 4\times {{10}^{-5}}\times {{10}^{-6}}}{{{10}^{-7}}}=M $ $ M=3.2\,A{{m}^{2}} $