The motor effect, electric motors and loudspeakers

Physics · Magnetism and electromagnetism. 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 has its own magnetic field. Put the wire between the poles of a magnet and the two fields interact, so the wire and the magnet push on each other. This is the motor effect.

The force is greatest when the wire is at right angles to the field and zero when the wire is parallel to it. Fleming's left-hand rule gives the direction of the force.

In a motor, a coil sits in a magnetic field. The current flows in opposite directions on the two sides of the coil, so one side is pushed up and the other down, and the coil rotates. A split-ring commutator keeps it turning the same way.

Rules to remember

force = magnetic flux density × current × length (F = BIl): F in N, B in tesla (T), I in A, l in m.
F = BIl applies when the conductor is at right angles to the field.
Left hand: First finger = Field (north to south), seCond finger = Current (positive to negative), thuMb = Motion (force).
Bigger force: larger current, stronger field, longer length of wire in the field.
Reversing the current or the field reverses the force; reversing both leaves it unchanged.
The split-ring commutator reverses the current in the coil every half turn.
Loudspeaker: an alternating current in a coil in a magnetic field makes the cone vibrate, producing pressure variations (sound).

Common mistake

Students put the length into F = BIl in centimetres. Convert to metres first: 5.0 cm is 0.050 m.

Worked example

A 30 cm length of wire is at right angles to a magnetic field of flux density 0.40 T. The force on the wire is 0.060 N. What is the current in the wire?

Convert the length: 30 cm = 0.30 m.
Rearrange F = BIl: I = F ÷ (B × l).
I = 0.060 ÷ (0.40 × 0.30) = 0.060 ÷ 0.12 = 0.50 A.

Answer: 0.50 A

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