Charged Particles in Electric Fields

A charged particle in an electric field will experience a force on it that will cause it to move
If a charged particle remains stationary in a uniform electric field, it will move parallel to the electric field lines (along or against the field lines depending on its charge)
If a charged particle is in motion through a uniform electric field (e.g. between two charged parallel plates), it will experience a constant electric force and travel in a parabolic trajectory

Parabolic trajectory, downloadable AS & A Level Physics revision notes

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. WE Motion of Charges Particles - proton trajectory, downloadable AS & A Level Physics revision notes 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 from the equation for electric force, F which is proportional to the charge q

$F = E q$

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

Motion_of_Charged_Particles_Worked_example_Boron_trajectory, downloadable AS & A Level Physics revision notes

Exam 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.

Charged Particles in Electric Fields (HL IB Physics)

Revision Note