Geometrical information coded in Maxwell's equations: a review

• Daniel Baldomir ^[1] ; Manuel Pereiro ^[1] ; Juan Arias ^[1]
  1. [1] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 30, Nº 2, 2011, págs. 793-811
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Purpose – The purpose of this paper is to show how the geometrical information of Maxwell's equations is coded into the constitutive equations.

    Design/methodology/approach – The Maxwell's equations have been written with the tensorial algebra into a three‐dimensional Euclidean space and compared with the usual four‐dimensional relativistic approach.

    Findings – This simple geometry allows the finding of the relativistic information coded on the electric and magnetic fields, showing that they are not independent as relativity affirm obtaining their transformation for a moving inertial observer.

    Originality/value – The main value of the paper is to present a simple mathematical tool which enables the engineers or applied physicists to obtain the relativistic transformations of the fields without using four‐dimensional geometries and the more sophisticated mathematical techniques.