Question

# A short bar magnet is kept along the magnetic meridian with its north pole pointing north. A neutral point is located at a distance d from the centre. What is the ratio of magnetic inductions at a distance d/2 and 2d from the centre of the magnet on the equatorial line ?

A
9 : 64
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B
8:1
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C
9 : 56
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D
64 : 9
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Solution

## The correct option is A 8:1mag. field at a distance x on equitorial line:B=μ0/4π×M/(x2+l2)3/2Assuming l<<x=>B=k×M/x3When north pole of magnet is aligned with geographical north, neutral points exists on the equatorial line.At neutral point, B=−BH,x=d Net mag field = 0.Bd=kMd3=−BHB2d=kM(2d)3=−BH/8Bnet,2d=BH+B2d=7BH/8Similarly,Bd/2=kM(d/2)3=−8BHBnet,d/2=BH+Bd/2=−7BHFinding the required ratio,Bnet,d/2Bnet,2d=8

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