Editing Electromagnetic field (section)

=== Behavior of the fields in the absence of charges or currents ===
[[File:Onde electromagnetique.svg|thumb|upright=1.8|A [[linear polarization|linearly polarized]] electromagnetic [[plane wave]] propagating parallel to the z-axis is a possible solution for the [[electromagnetic wave equation]]s in [[free space]]. The [[electric field]], {{math|'''E'''}}, and the [[magnetic field]], {{math|'''B'''}}, are perpendicular to each other and the direction of propagation.|400x200px]]
[[Maxwell's equations]] can be combined to derive [[wave equation]]s.  The solutions of these equations take the form of an [[electromagnetic wave]].  In a volume of space not containing charges or currents ([[free space]]) – that is, where <math>\rho</math> and {{math|'''J'''}} are zero, the electric and magnetic fields satisfy these [[electromagnetic wave equation]]s:{{sfnp|ps=|Feynman|Leighton|Sands|1970|loc=[https://www.feynmanlectures.caltech.edu/II_20.html §20.1]}}{{sfnp|ps=|Cheng|1989|loc=Intermediate-level textbook}}
: <math> \left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{E} \ \ = \ \ 0</math>
: <math> \left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{B} \ \ = \ \ 0</math>

[[James Clerk Maxwell]] was the first to obtain this relationship by his completion of Maxwell's equations with the addition of a [[displacement current]] term to [[Ampere's circuital law]]. This unified the physical understanding of electricity, magnetism, and light: visible light is but one portion of the full range of electromagnetic waves, the [[electromagnetic spectrum]].