Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a TimeVarying Magnetic Field
Abstract
In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a timevarying 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:

 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 (ARPAE)
 OSTI Identifier:
 1433514
 Grant/Contract Number:
 AR0000411
 Resource Type:
 Accepted Manuscript
 Journal Name:
 IEEE Antennas and Propagation Magazine
 Additional Journal Information:
 Journal Volume: 60; Journal Issue: 1; Journal ID: ISSN 10459243
 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 TimeVarying 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 TimeVarying Magnetic Field. United States. https://doi.org/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 TimeVarying Magnetic Field". United States. https://doi.org/10.1109/MAP.2017.2774206. https://www.osti.gov/servlets/purl/1433514.
@article{osti_1433514,
title = {Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a TimeVarying 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 timevarying 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 = {2017},
month = {12}
}
Web of Science
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