Velocity Selector (OCR A Level Physics)

Charged Particles in a Velocity Selector

• A velocity selector is defined as:

  A device consisting of perpendicular electric and magnetic fields where charged particles with a specific velocity can be filtered

• Velocity selectors are used in devices, such as mass spectrometers, in order to produce a beam of charged particles all travelling at the same velocity

• The construction of a velocity selector consists of two horizontal oppositely charged plates situated in a vacuum chamber

  • The plates provide a uniform electric field with strength E between them

• There is also a uniform magnetic field with flux density B applied perpendicular to the electric field

  • If a beam of charged particles enter between the plates, they may all have the same charge but travel at different speeds v

• The electric force does not depend on the velocity: F_E = EQ

• However, the magnetic force does depend on the velocity: F_B = BQv

  • The magnetic force will be greater for particles which are travelling faster

• To select particles travelling at exactly the desired the speed v, the electric and magnetic force must therefore be equal, but in opposite directions

F_E = F_B

The particles travelling at the desired speed v will travel through undeflected due to the equal and opposite electric and magnetic forces on them

• The resultant force on the particles at speed v will be zero, so they will remain undeflected and pass straight through between the plates

• By equating the electric and magnetic force equations:

EQ = BQv

• The charge Q will cancel out on both sides to give the selected velocity v equation:

• Therefore, the speed v in which a particle will remain undeflected is found by the ratio of the electric and magnetic field strength

  • If a particle has a speed greater or less than v, the magnetic force will deflect it and collide with one of the charged plates

  • This would remove the particles in the beam that are not exactly at speed v

• Note: the gravitational force on the charged particles will be negligible compared to the electric and magnetic forces and therefore can be ignored in these calculations