Thin Ohmic or superconducting strip with an applied ac electric current

TL;DR

This paper analyzes the electrical and magnetic properties of long, thin strips with applied AC current, comparing Ohmic and superconducting cases, revealing how impedance and fields depend on resistivity, frequency, and London depth.

Contribution

It provides a detailed calculation of impedance, currents, and fields in thin strips considering both Ohmic and superconducting states, highlighting differences in skin effect and length dependence.

Findings

Resistance enhancement due to skin effect is weaker in thin Ohmic strips (logarithmic)

Inductance per unit length depends logarithmically on strip length

Sheet current and magnetic fields are independent of strip length

Abstract

The complex impedance, currents, and electric and magnetic fields are calculated as functions of resistivity and frequency or London depth for a long thin strip with applied ac current. Both Ohmic and superconducting strips are considered. While the inductance per unit length of the strip depends on the strip length logarithmically, the sheet current, magnetic field, resistance, and magnetic susceptibility are independent of this length. It is found that the enhancement of resistance by the skin effect in thin Ohmic strips is much weaker (logarithmic) than in thick wires.