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Points A and B are situated along the extended axis of a 2 cm long bar magnet at a distance x and 2 x cm respectively from the pole nearer to the points. The ratio of the magnetic field at A and B will be

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a

4: 1 exactly

b

8: 1 exactly

c

4 : 1 approximately

d

8 : 1 approximately

answer is D.

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Detailed Solution

B=μ04π2Mr3where r is the distance of the point from the centre of the magnet. HenceBA=μ04π×2M(x+1)3 and BB=μ04π×2M(2x+1)3∴BABB=(2x+1)3(x+1)3≈(2x)3x3≈8:1

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