Usually when research with charged particles is carried out, scientists need to study particles whose velocities are well defined. The way they resort to achieve this feat is by building an ion filter , which actually has the function of blocking particles whose velocities are different from the velocities determined by them.
According to the figure, we can verify that only the ions that enter with the correct speed can pass through the second hole. The other ions are deflected from their trajectory and collide with the cylinder walls.
The incoming ion with velocity v is subjected to a total force given by the vector sum of the electric and magnetic forces. In this type of filter, the forces, both magnetic and electric, have the same direction, but have opposite directions. When these two forces have the same value, that is, they have the same magnitude, the total force becomes zero. This happens when we have:
Only ions with velocity v = E/B will pass through the cylinder without suffering any force, leaving the exit hole. All ions that have different velocities will be subjected to a non-zero total force and will be deflected from the initial trajectory, missing the exit orifice. By controlling the electric field E inside the filter, it is possible to select the speed of the ions that can pass through it.