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Question

A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the center of the magnet. If BH=0.4 G, the magnetic moment of the magnet is (1 G=104 T)

A
28.80 J T1
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B
2.880 J T1
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C
2.880×103 J T1
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D
2.880×102 J T1
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Solution

The correct option is B 2.880 J T1
A neutral point is obtained when the magnetic field due to bar magnet balances the horizontal component of earth's magnetic field (BH).

BH points towards north along the magnetic meridian.

From the figure, we can see that net magnetic field at the point due to bar magnet will be
B=2B0sinθ
B=2μ04πmr2×7r
where
B0 magnetic flux density

m power of magnetic pole
θ angle made by B0 with the horizontal

Given, BH=0.4G=0.4×104 T

For neutral point,
B=BH
0.4×104=2×107×m×7(72+182)32×104
m=4×102×(373)3214


Magnetic moment of the bar magnet,
M=m×14 cm=m×14100
M=0.04×(373)3214×14100
M2.88 J/T

Hence, option (b) is correct.

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