Explain why a proton moving in a straight line at constant speed through a region of space where both a uniform electric field and a uniform magnetic field are present is possible, and outline what this tells us about the relative magnitudes and directions of the two fields.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A proton travels in a straight line at constant speed through a region where a uniform electric field and a uniform magnetic field both exist simultaneously.
Model answer (4 marks)
For a proton to move in a straight line at constant speed the net force must be zero.
1. The electric force on the proton is qE.
2. The magnetic force is qvB.
3. For the forces to cancel, |qE| = |qvB|.
4. The forces must act in opposite directions, so qE and qvB are anti‑parallel.
5. Hence the condition E = vB (or v = E/B) must be satisfied. This is the principle of a velocity selector – only particles with speed v = E/B are undeflected, independent of charge‑to‑mass ratio.
1. The electric force on the proton is qE.
2. The magnetic force is qvB.
3. For the forces to cancel, |qE| = |qvB|.
4. The forces must act in opposite directions, so qE and qvB are anti‑parallel.
5. Hence the condition E = vB (or v = E/B) must be satisfied. This is the principle of a velocity selector – only particles with speed v = E/B are undeflected, independent of charge‑to‑mass ratio.
Examiner tips
- State that net force must be zero; give the two forces; equate magnitudes; note opposite directions; mention velocity selector condition.
- Use correct symbols (q, E, v, B) and units; show the relationship v = E/B explicitly.
Common mistakes
- Failing to mention that the forces must be opposite in direction; Not equating the magnitudes of the forces; Using the wrong sign convention for the magnetic force (qvB instead of qvB×α).
Mark scheme (4 marks)
- For the proton to travel in a straight line at constant speed, the net force on it must be zero.
- The electric force (qE) and the magnetic force (qvB) must be equal in magnitude.
- The electric force and magnetic force must act in opposite directions to each other (so that they cancel).
- This arrangement acts as a velocity selector: only particles with speed v = E/B travel undeflected, regardless of their charge-to-mass ratio.
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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