# Lorentz force and velocity filter

In this topic we will discuss about Lorentz force and velocity filter.In which we will know different conditions for Lorentz force and complete explanation of velocity filter .

**Lorentz force-**

*The force experienced by a charged particle due to both electric and magnetic field at a space called Lorentz’s force .*

Suppose a charge particle of mass ‘m’ and charge ’q’ is moving in the both electric and magnetic field of Field intensity ’E’ and ‘B’ respectively.

Then force due to electric field is given as F_{e}= q E

And force due to magnetic field will be F_{b}= q v B sinϴ ( where ϴ is the angle between v and B).

Then, Lorentz force F = F_{E}+F_{B} = q( E + v B sinϴ)………………Eq.

Special cases –

**Case 1- When v , E and B all are collinear** –

In this case F_{e} = q E ,

And F_{b}= o ( since ϴ= 0 ; sin 0 = 0 )

acceleration a = F_{e}/m = qE/m ,

**case 2 – When v , E and B are mutually perpendicular to each other** –

then net force F = F_{e} +F_{b} = 0

therefore acceleration a= 0 . It means particle will move without any deflection with the same velocity .

**Velocity filter –**

*It is an arrangement of cross electric and magnetic field in a space which help to select from a beam , charged particles of given velocity irrespective of their charge and mass. *

It consist two slits S_{1} and S_{2} placed parallel , with common axis at some distance . Uniform electric field ( E ) and magnetic field(B) applied which are perpendicular to each other , which is shown in figure. When a beam of charged particles of different charges and masses after passing through S_{1} enters into the region where crossed electric and magnetic field are present . The particles which is moving with velocity ‘v’ the electrostatic force and magnetic force are equal and opposite , then q E = q v B ,

Or, v= E/B

Such kind of particles go without changes its path and filtered out the region through the slits S_{2}. Therefore the particles emerging from S_{2} will have the same velocity even though their charges and masses may be different.

Velocity filter is used in mass spectrograph which help to find the mass and specific charge of the charged particle.