Q.

A very long cylindrical wire of radius R carries a current  I0 uniformly distributed across the cross-section of the wire. Calculate the magnetic flux through a rectangle that has one side of length w running down the centre of the wire and another side of length R, as shown in figure.

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a

μ0I0w4π

b

μ0I0wR4π

c

μ0I0R4πw

d

None

answer is A.

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Detailed Solution

Let us consider a rectangular strip of width dr as shown in figure.Magnetic field B at the element can be obtained from Ampere's law∮B.dl=μ0InetB×2πr=μ0I0πR2πr2         B=μ0I0r2πR2∴ dϕ=Bwdrϕ=∫dϕ=μ0I0w2πR2∫0Rrdr=μ0I0w4π
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