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Related Concept Videos

Induced Electric Fields01:23

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The fact that emfs are induced in circuits implies that work is being done on the conduction electrons in the wires. What can possibly be the source of this work? We know that it’s neither a battery nor a magnetic field, as a battery does not have to be present in a circuit where current is induced, and magnetic fields never do any work on moving charges. The source of the work is in fact an electric field that is induced in the wires. For example, if a stationary conductor is placed in a...
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Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by time-varying magnetic fields. While the former is a conservative field, implying that no net work is done on a test charge if it goes around in a complete loop in the field, the latter is, by definition, not a conservative field; net work is done, and it is proportional to the rate of change of magnetic flux.
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The work done by an external force on a particle changes its kinetic energy. However, internal forces must also be considered for a system of interacting particles. The potential energy formulation helps formulate the effect of internal forces. The net work done by an external force can be written in terms of the total change of mechanical energy, which includes both kinetic and potential energies.
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An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge distribution. Specifically, the induced electric field is nonconservative because it does not work in moving a charge over a closed path. In contrast, the electrostatic field is conservative and does no net work over a closed path. Hence, electric potential can be associated with the electrostatic field but not the induced field. The following...
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James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his theory predicted “Electromagnetic waves”. He brought together all the work that had been done by brilliant physicists such as Oersted, Coulomb, Gauss, and Faraday and added his own insights to develop the overarching theory of electromagnetism. Maxwell’s equations, combined with the Lorentz force law, encompass all the laws...
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Electric and Magnetic Field Devices for Stimulation of Biological Tissues
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The work done by an external electromagnetic field.

Mingliang Zhang1, D A Drabold

  • 1Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA. zhangm@ohio.edu

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 18, 2011
PubMed
Summary
This summary is machine-generated.

Ehrenfest's theorem provides a gauge-invariant power expression for external fields. The study analyzes the Kubo-Greenwood formula (KGF) for electrical conductivity, finding limitations in its conventional form for ab initio calculations.

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Area of Science:

  • Condensed matter physics
  • Theoretical physics

Background:

  • Ehrenfest's theorem relates forces to the time derivative of momentum.
  • Electrical conductivity calculations are crucial for materials science.
  • Gauge invariance is a fundamental principle in electromagnetism.

Purpose of the Study:

  • To derive a gauge-invariant expression for the rate of change of kinetic energy.
  • To analyze the validity and limitations of the Kubo-Greenwood formula (KGF) for electrical conductivity.
  • To assess the applicability of KGF in ab initio computational codes.

Main Methods:

  • Application of Ehrenfest's theorem to derive power expressions.
  • Analysis of the Mott-Davis and Moseley-Lukes forms of the Kubo-Greenwood formula.
  • Investigation of gauge invariance properties of the KGF.

Main Results:

  • A general expression for power induced by external electromagnetic fields, valid in any gauge.
  • Demonstration that the conventional Kubo-Greenwood formula lacks gauge invariance.
  • Identification of conditions under which the conventional KGF is applicable (high frequency, small carrier density gradient).

Conclusions:

  • The derived power expression offers a robust framework for studying energy changes in external fields.
  • The conventional Kubo-Greenwood formula requires careful consideration of its limitations for accurate ab initio calculations of electrical conductivity.