1
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Question

# A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio o the magnetic fields B and Bâ€², at radial distances a2 and 2a respectively, from the axis of the wire is

A
14
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B
12
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C
1
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D
4
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Solution

## The correct option is A 1Consider two amperian loops of radius a/2 and 2a as shown in the diagram.Applying ampere's circuital law for these loops, we get∮B.dL=μ0IenclosedFor the smaller loop,⇒B×2πa2=μ0×1πa2×(a2)2=μ0I×14=μ0I4⇒B1=μ0I4πaB′×2π(2a)=μ0IBB′=μ0I4πa×4πaμ0I=1Hence,option (C) is correct answer.

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