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Title: Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

Abstract

In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numerical simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.

Authors:
ORCiD logo [1]
  1. Univ. of Utah, Salt Lake City, UT (United States). Metallurgical Engineering
Publication Date:
Research Org.:
Univ. of Utah, Salt Lake City, UT (United States)
Sponsoring Org.:
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
OSTI Identifier:
1433514
Grant/Contract Number:
AR0000411
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
IEEE Antennas and Propagation Magazine
Additional Journal Information:
Journal Volume: 60; Journal Issue: 1; Journal ID: ISSN 1045-9243
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; 36 MATERIALS SCIENCE; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; eddy currents; quasistatics; current density

Citation Formats

Nagel, James R. Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field. United States: N. p., 2017. Web. doi:10.1109/MAP.2017.2774206.
Nagel, James R. Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field. United States. doi:10.1109/MAP.2017.2774206.
Nagel, James R. Fri . "Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field". United States. doi:10.1109/MAP.2017.2774206.
@article{osti_1433514,
title = {Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field},
author = {Nagel, James R.},
abstractNote = {In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numerical simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.},
doi = {10.1109/MAP.2017.2774206},
journal = {IEEE Antennas and Propagation Magazine},
number = 1,
volume = 60,
place = {United States},
year = {Fri Dec 22 00:00:00 EST 2017},
month = {Fri Dec 22 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on December 22, 2018
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