[[Electrodynamics MOC]]
# Electromagnetic momentum equation

The **momentum equation** states local momentum conservation for electrodynamics.
The rate at which momentum leaves charged matter in $\Omega$ equals the rate ofd 

$$
\begin{align*}
\frac{d\vab p_{\Omega}}{dt} = - \frac{d}{dt}\iiint_{\Omega}\vab g \,d\tau + \oiint_{\partial\Omega} \mathbf{T} \, d\vab a
\end{align*}
$$
where  $\vab g$ is [[Electromagnetic momentum density|momentum density]] $\mathbf{T}$ is the [[Maxwell stress tensor]]
$$
\begin{align*}
T_{ij} = \epsilon_{0}\left( E_{i}E_{j}-\frac{1}{2}\delta_{ij}E^2 \right)+\frac{1}{\mu_{0}}\left( B_{i}B_{j}-\frac{1}{2}\delta_{ij}B^2 \right)
\end{align*}
$$


[^2023]: 2023\. [[Sources/@grassoElectromagnetismSpecialRelativity2023|Electromagnetism and special relativity]], p. 79


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