Cem CivelekThomas Franz BechtelerBechteler, Thomas FranzCivelek, Cem2025-10-0620080080316611002072250020-72251879-219710.1016/j.ijengsci.2008.06.0072-s2.0-56349083625https://www.scopus.com/inward/record.uri?eid=2-s2.0-56349083625&doi=10.1016%2Fj.ijengsci.2008.06.007&partnerID=40&md5=08a2f5276c6191a982d4ed5540b24d14https://gcris.yasar.edu.tr/handle/123456789/10350https://doi.org/10.1016/j.ijengsci.2008.06.007This work is concerned with the Lagrangian formulation of electromagnetic fields. Here the extended Euler-Lagrange differential equation for continuous nondispersive media is employed. The Lagrangian density for electromagnetic fields is extended to derive all four Maxwell's equations by means of electric and magnetic potentials. For the first time ohmic losses for time and space variant fields are included. Therefore a dissipation density function with time dependent and gradient dependent terms is developed. Both the Lagrangian density and the dissipation density functions obey the extended Euler-Lagrange differential equation. Finally two examples demonstrate the advantage of describing interacting physical systems by a single Lagrangian density. © 2008 Elsevier Ltd. All rights reserved. © 2008 Elsevier B.V. All rights reserved.Englishinfo:eu-repo/semantics/closedAccessElectromagnetic Potentials, Euler-lagrange Differential Equation, Lagrangian Density, Maxwell's Equations, Electric Fields, Electromagnetic Field Measurement, Electromagnetic Fields, Electromagnetic Waves, Electromagnetism, Euler Equations, Lagrange Multipliers, Magnetic Materials, Probability Density Function, Density Functions, Electromagnetic Potentials, Euler-lagrange Differential Equation, Lag Ranges, Lagrangian Densities, Lagrangian Density, Lagrangian Formulations, Magnetic Potentials, Maxwell's Equations, Ohmic Losses, Physical Systems, Time Dependents, Maxwell EquationsElectric fields, Electromagnetic field measurement, Electromagnetic fields, Electromagnetic waves, Electromagnetism, Euler equations, Lagrange multipliers, Magnetic materials, Probability density function, Density functions, Electromagnetic potentials, Euler-Lagrange differential equation, Lag ranges, Lagrangian densities, Lagrangian density, Lagrangian formulations, Magnetic potentials, Maxwell's equations, Ohmic losses, Physical systems, Time dependents, Maxwell equationsElectromagnetic PotentialsEuler-Lagrange Differential EquationMaxwell’s EquationsLagrangian DensityArticle