AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Force on charged particles moving in a magnetic field, F = BQv when the…
Full specification wording
Moving charges in a magnetic field (A-level only): Force on charged particles moving in a magnetic field, F = BQv when the field is perpendicular to velocity.
A charged particle moving through a magnetic field experiences a force only when its velocity has a component perpendicular to the field.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 1 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A charged particle moving through a magnetic field experiences a force only when its velocity has a component perpendicular to the field. When the field is perpendicular to the velocity, the force magnitude is F = BQv, where B is flux density, Q is charge and v is speed. The force is always perpendicular to both the velocity and the field, so it does no work and changes direction but not speed. This produces circular motion: the magnetic force provides the centripetal force, so BQv = mv²/r and r = mv/(BQ). The direction follows Fleming's left-hand rule for positive charges; for negative charges the force is opposite. This explains mass spectrometers, cyclotrons and the helical paths of cosmic rays.
What earns the marks
- States that the force acts only on a moving charge and is zero when the velocity is parallel to the magnetic field.
- Applies F = BQv when the field is perpendicular to the velocity, substituting charge, flux density and speed with consistent units.
- Explains that the force is perpendicular to both velocity and field, so it does no work and the speed remains constant.
- Derives or uses BQv = mv²/r to find the radius of the circular path, r = mv/(BQ), for a charged particle in a perpendicular field.
- Determines the direction of the force using Fleming's left-hand rule, reversing the direction for negative charges.
- Describes applications such as the mass spectrometer or cyclotron, linking the radius to mass-to-charge ratio.
Common mistakes and how to put them right
Using F = BQv when the velocity is not perpendicular to the field.
Put it right: Use only the perpendicular component of velocity, or the full vector expression.
Treating the magnetic force as changing the particle's speed.
Put it right: Recognise that the force is always perpendicular to velocity, so it changes direction only.
Applying Fleming's left-hand rule without reversing for a negative charge.
Put it right: Reverse the predicted force direction for electrons and other negative particles.
Exam tips
- Check the geometry first: if the velocity is parallel to the field, the force is zero, and if perpendicular, use F = BQv directly.
- When asked for the radius, start from the centripetal force condition BQv = mv²/r and rearrange carefully, cancelling v where possible.
- Show the direction reasoning explicitly, stating that the force is perpendicular to both v and B and reversing for negative charge.
Try the lesson
The start of the Moving charges in a magnetic field (A-level only): Force on charged particles moving in a magnetic field, F = BQv when the field is perpendicular to velocity. lesson, made from checked teaching notes for this specification point.
Have a go first
A charged particle moves through a uniform magnetic field. The velocity of the particle is perpendicular to the magnetic field lines. Which quantity does the magnetic force on the particle depend on, in addition to the flux density and the speed of the particle?
Listen
A charged particle moving through a magnetic field experiences a force only when its velocity has a component perpendicular to the field. When the field is perpendicular to the velocity, the force magnitude is F = BQv, where B is flux density, Q is charge and v is speed. The force is always perpendicular to both the velocity and the field, so it does no work and changes direction but not speed. This produces circular motion: the magnetic force provides the centripetal force, so BQv = mv²/r and r = mv/(BQ). The direction follows Fleming's left-hand rule for positive charges; for negative charges the force is opposite. This explains mass spectrometers, cyclotrons and the helical paths of cosmic rays. A strong answer earns marks for these points. States that the force acts only on a moving charge and is zero when the velocity is parallel to the magnetic field. Applies F = BQv when the field is perpendicular to the velocity, substituting charge, flux density and speed with consistent units. Explains that the force is perpendicular to both velocity and field, so it does no work and the speed remains constant. Derives or uses BQv = mv²/r to find the radius of the circular path, r = mv/(BQ), for a charged particle in a perpendicular field. A common slip: Using F = BQv when the velocity is not perpendicular to the field. Instead, use only the perpendicular component of velocity, or the full vector expression. Exam tip: Check the geometry first: if the velocity is parallel to the field, the force is zero, and if perpendicular, use F = BQv directly.
Key words
Say what each word means before you turn the card.
Magnetic force on moving charges
Try answering aloud or in your head before turning the card.
Circular motion and centripetal force
Try answering aloud or in your head before turning the card.
Vector directions and the left-hand rule
Try answering aloud or in your head before turning the card.
Applications in particle physics
Try answering aloud or in your head before turning the card.
See every definition
- Magnetic force on moving charges
- A charged particle moving through a magnetic field experiences a force only when its velocity has a component perpendicular to the field.
- Circular motion and centripetal force
- The magnetic force provides the centripetal force, so BQv = mv²/r and r = mv/(BQ).
- Vector directions and the left-hand rule
- The force is always perpendicular to both the velocity and the field, and the direction follows Fleming's left-hand rule for positive charges; for negative charges the force is opposite.
- Applications in particle physics
- This explains mass spectrometers, cyclotrons and the helical paths of cosmic rays.
There is more to this lesson
The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Test your understanding of Moving charges in a magnetic field (A-level only): Force on charged particles moving in a magnetic field, F = BQv when the field is perpendicular to velocity.
Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge