Motion of charged particles
- A charged particle in a uniform electric field will experience a force on it that will cause it to move
- If the charge is stationary, it will move parallel to the field lines (along or against the field lines depending on its charge)
- If the charge is in motion (perpendicular to the field lines), it will experience a constant force and travel in a parabolic trajectory
The parabolic path of charged particles in a uniform electric field
- The direction of the parabola will depend on the charge of the particle
- A positive charge will be deflected towards the negative plate
- A negative charge will be deflected towards the positive plate
- The force on the particle is the same at all points and is always in the same direction
- Note: an uncharged particle, such as a neutron experiences no force in an electric field and will therefore travel straight through the plates undeflected
- The amount of deflection depends on the following properties of the particles:
- Mass – the greater the mass, the smaller the deflection and vice versa
- Charge – the greater the magnitude of the charge of the particle, the greater the deflection and vice versa
- Speed – the greater the speed of the particle, the smaller the deflection and vice versa
Worked example
A single proton travelling with a constant horizontal velocity enters a uniform electric field between two parallel charged plates.
The diagram shows the path taken by the proton.
Draw the path taken by a boron nucleus that enters the electric field at the same point and with the same velocity as the proton.
Atomic number of boron = 5
Mass number of boron = 11
Answer:
Step 1: Compare the charge of the boron nucleus to the proton
- Boron has 5 protons, meaning it has a charge 5 × greater than the proton
- The force on boron will therefore be 5 × greater than on the proton
- This is because electric force F is proportional to the charge Q
Step 2: Compare the mass of the boron nucleus to the proton
- The boron nucleus has a mass of 11 nucleons meaning its mass is 11 × greater than the proton
- The boron nucleus will therefore be less deflected than the proton
Step 3: Draw the trajectory of the boron nucleus
- Since the mass comparison is much greater than the charge comparison, the boron nucleus will be much less deflected than the proton
- The nucleus is positively charged since the neutrons in the nucleus have no charge
- Therefore, the shape of the path will be the same as the proton
Examiner Tip
Remember less deflection (e.g. from a higher mass particle) means the particle hits the plate later and the path has a smaller curve. Think of it as the particle being heavier so it is harder to steer it towards the plate.