# Fundamental Physics/Electromagnetism/Electromagnetic oscillation wave

## Electromagnetic oscillation wave

Electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light. The oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave.

Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with other charged particles

## Maxwell Vector equation of electromagnetic oscillation

${\displaystyle \nabla \cdot E=0}$
${\displaystyle \nabla \times E=-{\frac {1}{T}}E}$
${\displaystyle \nabla \cdot B=0}$
${\displaystyle \nabla \times B=-{\frac {1}{T}}B}$
${\displaystyle T=\mu \epsilon }$

## Electromagnetic wave

Using partial differential math

${\displaystyle \nabla (\nabla \times E)=\nabla (-{\frac {1}{T}}E)}$
${\displaystyle \nabla ^{2}E=-\omega E}$
${\displaystyle \nabla (\nabla \times B)=\nabla (-{\frac {1}{T}}B)}$
${\displaystyle \nabla ^{2}B=-\omega B}$

Electromagnetic wave equation

${\displaystyle \nabla ^{2}E=-\omega E}$
${\displaystyle \nabla ^{2}B=-\omega B}$

Electromagnetic wave function

${\displaystyle E=ASin\omega t}$
${\displaystyle B=ASin\omega t}$
${\displaystyle \omega =\lambda f={\sqrt {\frac {1}{T}}}=C}$
${\displaystyle T=\mu \epsilon }$