When a charged particle q moving with a velocity v in presence of both electric and magnetic fields.
The force experienced due to electric field `F_(E)=q vecE`
The force experinced due to magnetic field `F_(B)=q(vecvxxvecB).`
Consider electric and magnetic fields are perpenduclar to each other and also perpendicualr to the velocity of the particle.
`E= E hatj, B = B hatk, v= v hati`
`F_(E)=qE hatj, F_(B)=q(v hatixx Bhatk)=-qvB hatj`
`therefore F=F_(E)+F_(B)`
`F=q(E-vB) hatj`
Thus electric and magnetic forces are in opposite directions. We adjust E and B such that, the forces are equal
`F_(E)=F_(B)`
`q_(E)=q v B`
`v=(E)/(B)`
This condition can be used to select charged particles of a particular velocity. The crossed field E and B serve as a velocity selector.
