From Ampere's circuital law, for a long straight wire of circular cross-section carrying a steady current, the variation of the magnetic field in the inside and outside regions of the wire is

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(3) A linearly increasing function of distance r up to the boundary of the wire and then decreasing one with 1/r dependence for the outside region.. Idea: apply ∮⃗B· d⃗l=μ₀I_enc on a circle of radius r about the axis. Inside, r<R: the enclosed current is I(r²)/(R²), so B(2π r)=μ₀I(r²)/(R²). That gives B=(μ₀Ir)/(2π R²), proportional to r. Outside, r>R: the whole current is enclosed, so B(2π r)=μ₀I. That gives B=(μ₀I)/(2π r), falling as 1/r. So it rises linearly to the surface and then falls off as 1/r.

From Ampere's circuital law, for a long straight wire of circular cross-section carrying a steady current, the variation of the magnetic field in the inside and outside regions of the wire is

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