Motion of Charged Particle in Combined Uniform Electric and Magnetic Fields —
When a charged particle of charge $q$ moving with velocity $\vec{v}$ is subjected to an electric field $\vec{E}$ and magnetic field $\vec{B}$, the total force acting on the particle is
$\vec{F}=\vec{F}_E+\vec{F}_M=q \vec{E}+q(\vec{v} \times \vec{B})=q(\vec{E}+\vec{v} \times \vec{B})$
This force is known as Lorente force and is named after the Dutch physicist Hendrik Antoon Lorentz.
