Wien filter

Any charged particle in an electric field will feel a force proportional to the charge and field strength such that ${\displaystyle {\vec {F}}=q{\vec {E}}}$, where F is force, q is charge, and E is electric field strength. Similarly, any particle moving in a magnetic field will feel a force proportional to the velocity and charge of the particle. The force felt by any particle is then equal to ${\displaystyle {\vec {F}}=q{\vec {v}}\times {\vec {B}}}$, where F is force, q is the charge on the particle, v is the velocity of the particle, B is the strength of the magnetic field, and ${\displaystyle \times }$ is the cross product. In the case of a velocity selector, the magnetic field is always at 90 degrees to the velocity and the force is simplified to ${\displaystyle F=qvB}$ in the direction described by the cross product.

Setting the two forces to equal magnitude in opposite directions it can be shown that ${\displaystyle {\frac {E}{B}}=v}$. Which means that any combination of electric (${\displaystyle {\vec {E}}}$) and magnetic (${\displaystyle {\vec {B}}}$) fields will allow charged particles with only velocity ${\displaystyle {\vec {v}}}$ through.

• Neutron velocity selector