P7.3 The motor effect

The force on a current-carrying conductor

When a conductor carrying an electric current is placed in an external magnetic field, it experiences a force. This is called the motor effect. It happens because the magnetic field created by the current interacts with the external magnetic field.

The force is:

• Perpendicular to both the current and the magnetic field.
• Zero if the conductor is parallel to the field.
• Maximum if the conductor is perpendicular to the field.

Calculating the force: F = BIl

The magnitude of the force is given by:

F = BIl

where:

• F = force in newtons (N)
• B = magnetic flux density in teslas (T)
• I = current in amperes A
• l = length of conductor in the field (m)

Fleming's left-hand rule

The direction of the force is found using Fleming's left-hand rule:

• First finger (index) → direction of magnetic Field (N to S)
• seCond finger (middle) → direction of conventional Current
• thuMb → direction of Motion (force on conductor)

The DC motor

A rectangular coil of wire in a magnetic field spins when current flows through it (each side experiences a force in opposite directions — creating a turning effect). A split-ring commutator reverses the current direction every half-turn so the coil always spins in the same direction.

The loudspeaker

An AC current through a coil in a permanent magnet creates an alternating force on the coil, which vibrates a paper cone to produce sound. The frequency of the AC equals the frequency of the sound produced.

Exam tips

• Remember: left-hand rule for motors (force/motion). Right-hand rule is for generators — that is a different context.
• Units of B are teslas (T). A typical horseshoe magnet is 0.1–1 T.