Using split-ring resonators to measure the electromagnetic properties of materials: An experiment for senior physics undergraduates

Abstract

A spilt-ring resonator experiment suitable for senior physics undergraduates is described and demonstrated in detail. The apparatus consists of a conducting hollow cylinder with a narrow slit along its length and can be accurately modelled as a series $LRC$ circuit. The resonance frequency and quality factor of the split-ring resonator are measured when the apparatus is suspended in air, submerged in water, and submerged in an aqueous solution of various concentrations of NaCl. The experimental results are used to extract the dielectric constant of water and to investigate the dependence of the resonator quality factor on the conductivity of the NaCl solution. The apparatus provides opportunities to experimentally examine radiative losses, complex permittivity, the electromagnetic skin depth, and cutoff frequencies of rf propagation in cylindrical waveguides, which are all concepts introduced in an undergraduate course in electrodynamics. To connect with current research, the use of split-ring resonators as a tool to precisely measure the electromagnetic properties of materials is emphasized