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.
Solution
Force in the presence of magnetic and electric field is given as
`vecF=q(vecE+vecv xx vecB)`
Consider that the electric and the magnetic field are perpendicular to each other and, also, perpendicular to the velocity of the particle.
`vecE=Ehatj,vecB=Bhatk,vecB,vecv=vhati`
Then we have :`vec(F_E)=qvecE=qEhatj, vec(F_B)=q vecv xx vecB, =q(vhatixxBhatk)=-qBhatj`
`therefore vecF=q(E-vB)hatj`
If we adjust the values of `vecE` and `vecB` such that magnitudes of the two forces are equal, then the total force on the charge will be zero and it will move in the fields undeflected. This happens when
qE = qvB
`therefore v=E/B`
The above condition can be used to select a charged particle of particular velocity from the charges moving with different speeds. Therefore, it is called velocity selector.
