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Related Concept Videos

Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Electromagnetic Waves01:30

Electromagnetic Waves

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 of electricity and...
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
Maxwell's Equation Of Electromagnetism01:29

Maxwell's Equation Of Electromagnetism

James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...

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Related Experiment Video

Updated: Jul 4, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Extended symmetrical classical electrodynamics.

A V Fedorov1, E G Kalashnikov

  • 1Ulyanovsk State University, Ulyanovsk, Russia. anatoly.federov@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces modified electrodynamics without point charges, incorporating induced charges and currents dependent on a vector k. This framework describes electric monopoles and reveals a discrete spectrum for vector k.

Related Experiment Videos

Last Updated: Jul 4, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Area of Science:

  • Theoretical Physics
  • Electrodynamics
  • Mathematical Physics

Background:

  • Classical electrodynamics relies on point charges.
  • A need exists for alternative electrodynamic models.
  • Electromagnetic fields are described by Maxwell's equations.

Purpose of the Study:

  • To present a modification of classical electrodynamics.
  • To investigate a model without ordinary point charges.
  • To analyze the behavior of electromagnetic fields in modified electrodynamics.

Main Methods:

  • Introduced additional terms for induced charges and currents.
  • Defined electromagnetic field vectors (E and B) using two four-potentials.
  • Formulated the Lagrangian for the modified electrodynamics.
  • Derived conditions for a single four-potential description.
  • Analyzed static modified electrodynamics for an electric monopole.

Main Results:

  • Modified equations include induced charges and currents dependent on vector k and electromagnetic fields.
  • Vector k components form a third-rank four-tensor.
  • Static modified electrodynamics describes the inner region of an electric monopole.
  • Boundary conditions at the monopole interface lead to a discrete spectrum for vector k.
  • Calculated electric/magnetic fields, energy, and angular momentum for the monopole.

Conclusions:

  • The modified electrodynamics provides a framework for fields without point charges.
  • The model successfully describes electric monopoles under specific conditions.
  • The discrete spectrum of vector k has implications for monopole properties.