Question

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

Answer 1

its simple
lets consider a charged particle q moving with velocity v experiencing both magnetic (B) and electric field(E) perpendicular to it
then it will experience force from both fields
lets the force from MF be
F=qvBsinø where ø is 90 so
F=qvB
and force due to EF be
F =qE
when we equat both considering both forces to be equal then
qvB=qE
v=E/B
so charged particles with velocity equal to E/B will not experience any deflection and hence can be selected easily

Answer 2

Velocity selector is an arrangement of cross electric and magnetic fields is a region which helps us to select from a beam, charged particles of the given velocity.

When a beam of charged particles of different charge and masses pass, through a region of crossed electric and magnetic field B each particle experience a force due to electric and magnetic field.

Then,

qE = Bvq              or, v = E/B

such particles go undeviated and filter out of the region.

Cheers!!