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.

IB DP Physics Standard Level (2023 syllabus) — D.3 Motion in electromagnetic fields · Explain · 4 marks · View as Markdown

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.

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)

  1. The electric field exerts a force on the charged particle (electric force = qE).
  2. The magnetic field exerts a force on the moving charged particle (magnetic force = qvB) directed opposite to the electric force.
  3. 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.
  4. 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).

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