AC Resistance of a Round Wire When the Skin Depth δ Is Comparable to the Radius a of the Wire

We have shown in Section 2.2 that the parameters α and β are given by δ⁻¹ in a good conductor. The approximations made in arriving at this result assumed that the loss tangent T = σ_c/ωε is large. Another way of stating the approximation is to say that the displacement current density j ω ε E ˜ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315272351/41040b79-9956-496a-ac34-683fa4364729/content/eqi2a_1.jpg"/> is neglected in comparison with the conduction current density σ c E ˜ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315272351/41040b79-9956-496a-ac34-683fa4364729/content/eqi2a_2.jpg"/> . The propagation constant γ = jk may be obtained in this case by neglecting the first term on the RHS of (2.4) 2A.1 γ 2 = − k 2 = j ω μ σ = 2 π f μ σ e j π / 2 . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315272351/41040b79-9956-496a-ac34-683fa4364729/content/eqn2a_1.jpg"/>