6.5.8 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

Part (a)

Step 1: Determine the direction of the E field

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

Step 2: Determine the direction of the B field

• • Using Fleming’s left-hand rule:
    • The charge or current I is directed to the right
    • B must be directed out of the page / screen for the magnetic force F to act vertically downwards

Part (b)

Step 1: List the known quantities

• • Electric field strength, E = 2.8 kV m⁻¹ = 2.8 × 10³ V m⁻¹
  • Magnetic flux density, B = 0.50 T

Step 2: Write down the velocity selector equation

Step 3: Calculate the speed of the ion at S

= 5600 m s⁻¹

Part (c)

Step 1: Consider the effect of changing the ion's speed on the electric and magnetic forces

• • Electric force is given by:

F_E = EQ

• • Therefore, electric force does not depend on the velocity 
  • Magnetic force is given by:

F_B = BQv

• • Therefore, F_B ∝ v, so if the speed increases, the magnetic force must increase to match the electric force 

Step 2: Determine the net direction of the force 

• • Since the net magnetic force would direct the ion downwards in the direction of the field
  • The ion will be deflected towards the positive plate