Velocity-selector (Wien filter)

Using a Wien filter is an easy way to select charged particles with a specific speed.

Setup:

The velocity-selector is a device consisting of perpendicular electric and magnetic fields. A plate capacitor, producing an electric field, is placed in a magnetic field. At the end of the plate capacitor is an aperture. So only particles moving in the middle of the device can pass the Wien filter.
Setup of a velocity-selector (Wien filter)
The particle beam enters the velocity-filter so that the velocity-vector of the particles, the electric field and the magnetic field are pairwise perpendicular to each other.

Function:

When entering the Wien filter electric and magnetic fields cause two different forces (weight force neglected).
The electic field causes the electric force (Coulomb-force) $F_{el}$:Setup of a velocity-selector (Wien filter) $$F_{el}=q\cdot E$$ The motion of charge in a magnetic field causes a Lorentz-force:$$F_{Lorentz}=q\cdot v\cdot B$$ Only particles, where the amount of electric force $F_{el}$ and Lorentz-force $F_{Lorentz}$ are equal and show in contrary directions, are not deflected in the velocity-filter. For those particles apply:$$F_{el}=F_{Lorentz}\qquad bzw.\qquad q\cdot E=q\cdot v\cdot B$$ Solveing for $v$ provides the velocity, the particles must have to pass the Wien filter: $$v_{\text{passage}}=\frac{E}{B}$$ By particles with velocity $v_0 < v_{\text{passage}}$ the force $F_{el}$ is bigger than $F_{Lorentz}$.
By particles with velocity $v_0 > v_{\text{passage}}$ the Lorentz-force $F_{Lorentz}$ is bigger than $F_{el}$.

Limitations:

Neither mass of the particles nor the charge of the particles are important for this velocity filter. All particles with the velocity $v_{\text{passage}}$ pass the Wien filter no matter of their mass and their charge.
Also all uncharged particles pass the filter, no matter of their velocity.