Explain why a charged particle moving at a constant velocity in a uniform electric field and a uniform magnetic field can travel in a straight line without deflection, and outline what condition must be satisfied for this to occur.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A beam of charged particles enters a region where a uniform electric field and a uniform magnetic field are directed perpendicular to each other and to the initial velocity of the particles.
Model answer (4 marks)
A charged particle experiences an electric force
F_E = qE
and a magnetic force
F_B = qvB
directed opposite to each other. When the magnitudes are equal, F_E = F_B, the net force is zero, so the particle continues in a straight line at constant velocity.
The condition for this is
qE = qvB → E = vB.
F_E = qE
and a magnetic force
F_B = qvB
directed opposite to each other. When the magnitudes are equal, F_E = F_B, the net force is zero, so the particle continues in a straight line at constant velocity.
The condition for this is
qE = qvB → E = vB.
Examiner tips
- Use the formulae for electric and magnetic forces; show the forces are opposite.
- State the equality of magnitudes and the resulting zero net force.
- Give the simplified condition E = vB.
- Mention that the particle’s speed must be such that v = E/B.
Common mistakes
- Confusing the direction of the magnetic force (using v×B instead of magnitude).
- Forgetting to cancel the charge q when simplifying the condition.
- Writing E = B/v instead of E = vB.
Mark scheme (4 marks)
- The electric field exerts a force on the charged particle (electric force = qE).
- The magnetic field exerts a force on the moving charged particle (magnetic force = qvB) directed opposite to the electric force.
- When the two forces are equal in magnitude, the net force on the particle is zero, so it continues in a straight line at constant velocity.
- The condition for straight-line travel is qE = qvB, which simplifies to E = vB (the electric field strength equals the product of the particle's speed and the magnetic flux density).
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
More Motion in electromagnetic fields questions
- Explain why a proton moving in a circle inside a cyclotron must be accelerated e…
- A positive ion moves horizontally to the right with constant velocity through a …
- A beam of electrons enters a region where a uniform magnetic field acts perpendi…
- A proton enters a uniform magnetic field directed into the page. The proton init…