Lorentz Force

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 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.