A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances a/2 and 2a respectively from the axis of the wire, is

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(1) 1. Given: one point inside at r=a/2 and one outside at r=2a. Idea: the two points sit in different regions, so they need different formulae. Inside: B=(μ₀Ir)/(2π a²), so at r=a/2, B=(μ₀I)/(4π a). Outside: B'=(μ₀I)/(2π r), so at r=2a, B'=(μ₀I)/(4π a). The two expressions are identical. B/(B')=1. Going half a radius in and twice a radius out happen to weaken the field by the same factor.

A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances a/2 and 2a respectively from the axis of the wire, is

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