Motion of Charged Particles (Cambridge International A-Level Physics)

Spec point — 18.2.2

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

$F=EQ$

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

Exam Hint 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.