Calculation of the Admittance of a Parallel Plate Capacitor Containing a Toroid-Shaped Sample (Classic Reprint) - Hardcover

Eric G. Johnson Jr.

9780365639039: Calculation of the Admittance of a Parallel Plate Capacitor Containing a Toroid-Shaped Sample (Classic Reprint)

Hardcover

ISBN 10: 0365639036 ISBN 13: 9780365639039

Publisher: Forgotten Books, 2018

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This book presents a complex calculation regarding the admittance of a parallel plate capacitor containing a toroid-shaped sample. The paper is exceptional because it corrects the usual quasi-static formula (zero-order solution) for characterizing a capacitor to at least second order in perturbation theory. The zero and first-order calculations occur under the assumption that there is no height dependence of the electromagnetic field. The formula, however, permits lossy materials (complex μ and ε) because the experiment utilizes a geometry where the sample is not in contact with the capacitor plates. As a result, it is necessary to make an educated guess regarding an effective permeability and permittivity for the zero and first-order solution to the problem. The second-order term primarily attempts to adjust for the effects of there being height dependence in the electromagnetic field. The theoretical admittance of a toroid-shaped sample in a parallel-plate capacitor system is developed, with the author demonstrating a first and second-order perturbation correction to the usual quasi-static formula. The depth of the analysis provides a solid foundation for comprehension of the complex relationship between a sample's properties and its behavior in a capacitor system.

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