A steady, uniform current density flows along through a wire of circular…

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Maxwell's equations and conservation laws

Invariance, Ch Integrating forms: Stokes's theorem, holes and Maxwell's equations

Problem

A steady, uniform current density J=2.0 A m−2J = 2.0\,\mathrm{A\,m^{-2}} flows along zz through a wire of circular cross-sectional area A=1.0×10−4 m2A = 1.0\times10^{-4}\,\mathrm{m^2}. There is no time-dependent electric field, so the Ampère-Maxwell equation reduces to its magnetostatic part. Using the fact that d⋆F=μ0⋆J\mathrm{d}{\star}F = \mu_0{\star}J integrates, by the generalised Stokes theorem, to ∮B⋅dl=μ0Ienc\oint\mathbf{B}\cdot\mathrm{d}\mathbf{l} = \mu_0I_{\text{enc}} for a loop of winding number 11 round the wire, find ∮B⋅dl\oint\mathbf{B}\cdot\mathrm{d}\mathbf{l} for such a loop, with μ0=4π×10−7 T m A−1\mu_0 = 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}}.

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