Particles in an Electromagnetic Field

  • Alberto Galindo
  • Pedro Pascual
Part of the Texts and Monographs in Physics book series (TMP)


It is well known [JA 75] that in classical electrodynamics, an electromagnetic field is described by the electric and magnetic fields E(r; t),B(r; t). These fields satisfy Maxwell’s equations, which in unrationalized Gaussian units become
$$\begin{gathered}\nabla \times E\left( {r;t} \right) + \frac{1}{c}\frac{{\partial B\left( {r;t} \right)}}{{\partial t}} = 0, \hfill \\\nabla \cdot E\left( {r;t} \right) = 4\pi {\ell _e}\left( {r;t} \right), \hfill \\\nabla \times B\left( {r;t} \right) - \frac{1}{c}\frac{{\partial E\left( {r;t} \right)}}{{\partial t}} = \frac{{4\pi }}{c}{J_{em}}\left( {r;t} \right), \hfill \\\end{gathered} $$
where ϱe(r; t) and J em (r; t) are respectively the charge and current densities, related by the continuity equation
$$\frac{{{\partial _{{\varrho _e}}}\left( {r;t} \right)}}{{\partial t}} + \nabla \cdot{J_{em}}\left( {r;t} \right) = 0$$


Helium Kato 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alberto Galindo
    • 1
  • Pedro Pascual
    • 2
  1. 1.Facultad de Ciencias Físicas, Departamento de Física TeóricaUniversidad ComplutenseMadridSpain
  2. 2.Facultad de Física, Departamento de Física TeóricaUniversidad de BarcelonaBarcelonaSpain

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