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:ID:       658f3916-6b7f-4897-85c6-9acc82b13214
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#+title: Lorentz Force
#+author: Preston Pan
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* Definition
The Lorentz Force is an experimental law given by the equation:
\begin{align*}
\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})
\end{align*}
Where $q$ is the electric charge, $\vec{E}$ is the [[id:63656810-537f-42fc-a38a-1468d763b39a][Electric Field]], and $\vec{B}$ is the Magnetic Field.
For a continuous charge distribution:
\begin{align*}
\vec{F} = \rho\vec{E} + \vec{J} \times \vec{B}
\end{align*}
Where $\vec{J}$ is the electric current.