Velocity selection
- 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, to produce a beam of charged particles all travelling at the same velocity
- A velocity selector consists of two oppositely charged parallel 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 enters between the plates, they may all have the same charge Q but travel at different speeds
Velocity selector
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 electric force does not depend on the velocity:
- However, the magnetic force does depend on the velocity:
- The magnetic force will be greater for particles which are travelling faster
- To select particles travelling at exactly the desired speed v, the electric and magnetic force must therefore be equal, but in opposite directions
- 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:
- 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
Worked example
A positive ion travels between two charged plates towards a slit S
(a) State the direction of the electric and magnetic fields on the ion
(b) Calculate the speed of the ion emerging from slit S when the magnetic flux density is 0.50 T and the electric field strength is 2.8 kV m-1
(c) Which plate will the ion be deflected towards if the speed was greater than the speed in part (b)
Answer:
Part (a)
Step 1: Determine the direction of 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 B field
- Using Fleming’s left-hand rule:
- The charge, or current I, is directed to the right
- B is out of the page
- Therefore, the force F is vertically downwards
Part (b)
- 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 FB ∝ 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