As we know that a charged Q moving with velocity V in the presence of both electric and magnetic field experiences a force given by
We should consider the simple case in which electric and magnetic fields are perpendicular to each other and also perpendicular to the velocity of the particle, as shown in figure
Therefore, F = q ( E – vB ) j^
Thus electric and magnetic forces are in opposite direction as shown in figure. Suppose we adjust the value of E and B such that magnitude of two forces are equal.
Then, total force on the charge is zero as the charge will move in the fields undeflected.
This happens when –
qE = qvB or v = E/B
His condition can be used to select charged particle of a particular velocity out of a beam on charges moving with different speeds
( irrespective of their charge and mass ).
The crossed E and B fields, therefore, serve as a velocity selector.
Only particles with speed E/B pass undeflected through the region of cross fields.
This method was employed by JJ Thomson in 1897 to measure the charge to mass ratio of an electron.
The principle is also employed in mass spectrometer which is the device that separate charged particles, usually ions, according to their charge to mass ratio.