A positive ion moves horizontally to the right with constant velocity through a region where both a uniform electric field and a uniform magnetic field are present. The electric field acts vertically downward and the magnetic field acts perpendicularly into the page. Explain how the magnitudes and directions of the two forces acting on the ion combine to allow it to travel in a straight line at constant velocity, and state what happens to the ion's path if it then enters a region where only the magnetic field remains.

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).

Model answer (4 marks)

The electric field exerts a downward force on the positive ion (F_E = qE, downward). The magnetic field, into the page, gives an upward force on the ion moving right (F_B = qvB, upward by Fleming’s left‑hand rule). The two forces are equal in magnitude and opposite in direction, so the net force is zero and the ion moves in a straight line at constant velocity – the velocity‑selector condition qE = qvB, giving v = E/B.

If the ion then enters a region with only the magnetic field, the electric force disappears. The remaining magnetic force is always perpendicular to the velocity, providing a centripetal force but doing no work, so the ion follows a circular (curved) path.

Examiner tips

  • Show the direction of each force using the correct rule (F = qE, Fleming’s left‑hand rule).
  • State the velocity‑selector condition qE = qvB to justify equal magnitudes.
  • Explain that the magnetic force is perpendicular to velocity, so it changes direction but not speed.
  • Mention that the ion will then move in a circle because the magnetic force is centripetal and does no work.

Common mistakes

  • Using the wrong direction for the magnetic force (e.g. downward instead of upward).
  • Failing to state the velocity‑selector condition or the equality of magnitudes.
  • Not recognising that the magnetic force does no work and therefore the speed remains constant in the magnetic‑only region.

Mark scheme (4 marks)

  1. The electric field exerts a downward force on the positive ion (F = qE, directed downward).
  2. The magnetic force on the ion moving right in a field into the page acts vertically upward (by Fleming's left-hand rule / F = qv × B).
  3. The two forces are equal in magnitude and opposite in direction, so the net force is zero and the ion travels in a straight line at constant velocity (velocity selector condition: qE = qvB, so v = E/B).
  4. In the region with only the magnetic field, the ion follows a circular (curved) path because the magnetic force is always perpendicular to the velocity, providing a centripetal force but doing no work.

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