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

arXiv comment10 pages, 7 figures

References in corpus (6)

• Magnetic Penetration Depth in Unconventional Superconductors
• Microwave Electrodynamics of Electron-Doped Cuprate Superconductors
• Permittivity measurements of biological samples by an open-ended coaxial line
• Single Superconducting Split-Ring Resonator Electrodynamics
• Precision Microwave Electrodynamic Measurements of K- and Co-doped BaFe${}_2$As${}_2$
• Permittivity of waste-activated sludge by an open-ended coaxial line

Cited by in corpus (9)

• Strongly Enhanced Sensitivity in Planar Microwave Sensors Based on Metamaterial coupling
• Permittivity and Conductivity Measured using a Novel Toroidal Split-Ring Resonator
• Ferromagnetic resonance in the complex permeability of an Fe${}_3$O${}_4$ nanosuspension at radio and microwave frequencies
• Mid-Range Wireless Power Transfer at 100 MHz using Magnetically-Coupled Loop-Gap Resonators
• Design and characterization of a novel toroidal split-ring resonator
• The Complex Permeability of Split-Ring Resonator Arrays Measured at Microwave Frequencies
• Probing Split-Ring Resonator Permeabilities with Loop-Gap Resonators
• Modeling and measuring the non-ideal characteristics of transmission lines
• Inductive Power Transfer Through Saltwater