In Thomson's experiment, when the magnetic force balanced the electric force, the velocity of the beam was

where E is the magnitude of the electric field and B the magnitude of the magnetic field.
Let's see why. The force exerted by the electric field of intensity E on each electron is

where

is the electron charge.
The force exerted by the magnetic field of intensity B on each electron is

where v is the speed of the electrons.
When the two forces are balanced, we have:

from which we find
