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