Question

A long straight wire of radius a carries a steady current I.
The current is uniformly distributed over its cross-section.
The ratio of the magnetic fields B and B', at radial distances
a/2 and 2a respectively, from the axis of the wire is :[2016]
(a) 1/4
(b) 1/2
(c) 1 (d) 4

Answer 1

Answer:

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 B′, at radial distances 2a and 2a respectively, from the axis of the wire is.

Explanation:

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Answer 2

Answer:

(c)1(d) 4

Explanation:

Consider 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=μ 0 I enclosed For the smaller loop,⇒B×2π 2a =μ 0 × πa 2 1 ×( 2a ) 2 =μ 0 I× 41 = 4μ 0 I ⇒B 1 = 4πaμ 0 I B ′ ×2π(2a)=μ 0 IB ′ B = 4πaμ 0 I × μ 0 I4πa