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Q.

A current i is uniformly distributed over the cross section of a cylindrical conductor of radius R. The flux through the shaded rectangular plane which passes through the axis due to the long straight current is

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a

μ0li4π

b

μ0li2π

c

μ0liπ

d

2μ0liπ

answer is A.

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Detailed Solution

Consider a strip along the axis at distance r and of thickness dr. In this strip magnetic field is Bin=(μ02πiR2)r∴Magnetic Flux, ϕ=∫B→in.dA→0R=∫0Rμ02πiR2⋅r×ldr=μ0li4π
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