Velocity Selector

prerequisite materials

Definition of the force in an electric field, $F=qE$

Magnetic Field Strength, $F=qvB$

Derivation of the Velocity Selector Equation

The forces on the charged particle passing through the velocity selector due to the electric, $E$, and magnetic field, $B$, are opposite directions. For a particle of the selected velocity these forces are also equal in size.

$${\mathbf{F}}_E={\mathbf{F}}_B$$ $$\therefore qE=qvB$$ $$\Rightarrow E=vB$$ $$v=\frac{E}{B}$$

Follow on and further study:

Mass Spectrometer