Classical Electrodynamics · Problem Ex-5.17

Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws — John David Jackson

Physics — E&M · two-wire-self-inductance-per-unit-length

Problem

Consider a circuit made up of two long, parallel, nonpermeable, circular wires of radii a1a_1 and a2a_2, separated by a distance dd large compared to the largest radius. Current flows up one wire and back along the other. Ignore the ends. Use the method above to show that the self-inductance per unit length is approximately dLdl≈μ0π[ln⁡(ξda1a2)+14]\frac{dL}{dl} \approx \frac{\mu_0}{\pi}\left[\ln\left(\frac{\xi d}{\sqrt{a_1 a_2}}\right) + \frac{1}{4}\right] where ξ\xi is of order unity. Can you find a reliable value of ξ\xi, within the approximations stated?

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