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 because electric force F 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

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.

Charged Particles in Electric Fields (HL IB Physics)

Revision Note