Explain why two long, parallel wires carrying currents in the same direction attract each other.

IB DP Physics Standard Level (2023 syllabus) — D.2 Electric and magnetic fields · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Two long, straight parallel conducting wires are separated by a small distance. Each wire carries a steady direct current flowing in the same direction.

Model answer (4 marks)

Each current‑carrying wire creates a magnetic field that circles the wire (right‑hand rule). The field produced by wire A at the position of wire B is directed perpendicular to the line joining the wires, pointing from B towards A. Wire B carries a current I in the same direction as wire A, so it experiences a magnetic force
F = I L × B. Using Fleming’s left‑hand rule or the cross‑product, the force on B is directed towards A. By Newton’s third law, wire A experiences an equal and opposite force, so both wires are attracted to each other.

Examiner tips

  • Use the right‑hand rule to state the direction of the magnetic field around each wire.
  • Show that the field at the other wire is perpendicular to the current and points towards the first wire.
  • Apply F = I L × B (or Fleming’s left‑hand rule) to give the force direction.
  • Mention Newton’s third law to justify equal and opposite forces.

Common mistakes

  • Confusing the direction of the magnetic field (using left‑hand rule instead of right‑hand rule).
  • Forgetting that the force is perpendicular to both the current and the magnetic field.
  • Failing to state that the forces on the two wires are equal and opposite.

Mark scheme (4 marks)

  1. Each current-carrying wire produces a magnetic field in the space around it.
  2. The magnetic field lines produced by one wire are circular and directed (using the right-hand rule / corkscrew rule) such that the field at the location of the second wire is directed perpendicularly between the two wires.
  3. The second wire, carrying a current in that magnetic field, experiences a force given by F = BIL; the direction of the force (by Fleming's left-hand rule or F = IL × B) is towards the first wire.
  4. By Newton's third law (or by symmetry), each wire exerts an equal and opposite attractive force on the other, so both wires are pulled towards each other.

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