Theory
Any charged particle in an electric field will feel a force proportional to the charge and field strength such that, where F is force, q is charge, and E is electric field. 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, 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 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 in the direction described by the cross product.
Setting the two forces to equal magnitude in opposite directions it can be shown that . Which means that any combination of electric and magnetic fields will allow charged particles with only velocity through.
Read more about this topic: Velocity Selector
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