• 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

Part (a)

Step 1:????????????Direction of E field

• • • • • Electric field lines point from the positive to negative to charge
        • Therefore, it must be directed?vertically upwards

Step 2:??????????? Direction of B field

• • • • • Using?Fleming’s left-hand rule:
          • The charge or current I is to the right
          • B is out of the page
          • Therefore, the force F is?vertically downwards

Part (b)

Velocity selector equation

Electric field strength, E = 2.8 kV m^-1?=?2.8 × 10³?V m^-1

Magnetic flux density, B =?0.50 T

Part (c)

If the speed increases, the magnetic force must be greater because F_B?∝ v

Since the magnetic force would direct the ion downwards in the direction of the field, the ion will be deflected?towards the positive plate