Question

Find the condition under which the charged particles moving with different speeds in the presence of electric and magnetic field vectors can be used to select charged particles of a particular speed.

Answer 1

A charge q moving with velocity v in presence of both electric and magnetic fields experiences a force
$F=q(E+v\times B)$
Lets consider a simple case in which electric and magnetic fields are perpendicular to each other and also perpendicular to the velocity of the particle.
Electric and magnetic forces are in opposite directions and the values of E and B are adjusted in such a manner that magnitudes of the two forces are equal.
In such a situation,
$qE=qvB$ or $v=\frac{E}{B}$.
This condition can be used to select charged particles of a particular velocity out of a beam containing charges moving with different speeds(irrespective of their charge and mass).
The crossed E and B fields, therefore,serve as a velocity filter. Only particles with speed E/B pass undeflected through the region of crossed fields.