Force on a current-carrying conductor

Physics A2 · Magnetic fields. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A wire carrying a current in a magnetic field can feel a force. This is the motor effect. The force is greatest when the wire is at right angles to the field and is zero when the wire lies along the field.

The direction comes from Fleming's left-hand rule: first finger for the field, second finger for the conventional current, thumb for the force. The force is at right angles to both the field and the current.

This force is used to define magnetic flux density B, the strength of the field. By Newton's third law, the wire pushes back on the magnet with an equal and opposite force.

Rules to remember

Common mistake

θ is the angle between the wire and the field, not the angle to the perpendicular. Use the left hand, and L must be only the length of wire inside the field, in metres.

Worked example

A wire of length 0.12 m carries a current of 5.0 A at right angles to a uniform magnetic field. The force on the wire is 0.030 N. What is the flux density?

  1. The wire is perpendicular to the field, so F = BIL.
  2. Rearrange: B = F ÷ (IL) = 0.030 ÷ (5.0 × 0.12).
  3. B = 0.030 ÷ 0.60 = 0.050 T.

Answer: 0.050 T

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