= External inductance of a thin two-wire line
{title2=$L'_{\rm ext}\simeq\mu_0\ln(d/a_w)/\pi$}
Two long round wires of radius $a_w\ll d$ carrying opposite <electric currents> form a loop with the displayed leading external <self-inductance> per unit length. Integrating their summed <magnetic field> across a connecting ribbon gives the logarithm; magnetic-energy integration gives the same leading value. The zero-radius limit diverges. Uniform direct current inside two nonmagnetic round wires contributes another $\mu_0/(4\pi)$, while an ideal surface current has no interior contribution.
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