The Velocity Selector

The Lorentz force is the total force acting on a point charge due to external electric and magnetic fields.

\[\begin{equation} \vec{F} = q \left [ \vec{E} + \vec{v} \times \vec{B} \right ] \end{equation}\]

Under what conditions is the Lorentz force equal to zero? Well, if the electric force (\(q\vec{E}\)) on the charged particle is equal and opposite to the magnetic force (\(q\vec{v} \times \vec{B}\)) on the charged particle, then they will cancel each other out and the net force will equal zero. If the net force on the charged particle is zero, it will feel no acceleration. Thus, its velocity will not change; these are the conditions for a velocity selector.

In the video above, I derive an expression for the speed of a charged particle that will pass through a velocity selector undeflected.