2015 BFY II Abstract Detail Page
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||W03 - Using split-ring resonators to measure the electromagnetic properties of materials: An experiment for senior physics undergraduates
||In this experiment a split-ring resonator (SRR) is used to measure the dielectric constant of water and the conductivity of various concentrations of NaCl dissolved in water.
The SRR is made by cutting a narrow slit along the length of a conducting tube and can be modelled as a series-LRC circuit. The tube acts as a single-turn inductor and the slit as a parallel-plate capacitor. The inductance and capacitance, and hence resonance frequency, are determined by the dimensions of the SRR. The resistance of the SRR, which determines the quality factor (Q) of the resonance, is set by the skin depth of the conductor. An aluminum SRR has been constructed that, when immersed in air, has a resonance frequency and quality factor of 350 MHz and 2000 respectively.
Students first characterize the in-air properties of the SRR and compare the measurements to predictions. Two coupling loops are formed by shorting the inner conductor of a coaxial cable to the outer conductor. One loop is connected to a signal generator and suspended near one end of the SRR. This drive loop creates a changing magnetic flux in the SRR. Currents induced in the SRR in turn create a magnetic flux that can be detected by a second coupling loop placed at the opposite end of the SRR. The measured Q is much lower than predicted and this is due to radiative losses. These losses can be suppressed by suspending the SRR inside a conducting tube.
Next, students fill the outer tube with distilled water. The water fills the slit of the SRR and changes the effective capacitance by a factor equal to the dielectric constant of water. As a result of the large dielectric constant of water, there is a corresponding large change in the resonance frequency. The ratio of the measured in-air and in-water resonance frequencies is equal to the square root of the dielectric constant of water.
Finally, students can dissolve a known amount of NaCl in the water. The result is an additional ionic conduction across the gap of the capacitor. A relatively simple complex algebra analysis reveals that the ionic conductivity leaves the resonance frequency unchanged but enhances the effective resistance of the LRC circuit by an amount that is proportional to the conductivity of the saltwater solution. Thus, the decrease in the Q of the resonance is a measure of the conductivity of the water.
University of British Columbia, Okanagan Campus
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