Force on a current-carrying conductor

The motor effect

• A wire carrying a current in a magnetic field experiences a force.
• This is called the motor effect, and it is the principle behind every electric motor and loudspeaker.

$$F = BIL$$

• $F$ — force on the conductor (N)

• $B$ — magnetic field strength (tesla, T)

• $I$ — current in the conductor (A)

• $L$ — length of conductor in the field (m)

• The relationship as written applies when the current is perpendicular to the field.

• $L$ is the length inside the field, not the whole length of the wire.

When the force is zero

• The force is greatest when the current is at $90°$ to the field.
• The force is zero when the current is parallel to the field.
• This is worth stating in explanation answers: the effect depends entirely on the relative directions of the current and the field.

The direction: the left-hand motor rule

Using Fleming's left-hand rule, with the first three fingers of the left hand held mutually at right angles:

• First finger → Field (from N to S)

• seCond finger → Current (conventional current, positive to negative)

• thuMb → Motion (the force on the conductor)

• The three are mutually perpendicular — the force is always at right angles to both the field and the current.

• Use conventional current, not electron flow. If a question describes electron movement, reverse it first.

• Reversing either the current or the field reverses the force. Reversing both leaves it unchanged.

Drawing in three dimensions

Exam diagrams use standard symbols for directions perpendicular to the page:

• A dot (⊙) — pointing out of the page, toward you (the tip of an arrow).

• A cross (⊗) — pointing into the page, away from you (the tail feathers of an arrow).

• A grid of dots or crosses represents a uniform field perpendicular to the page.

• Practise the hand rule physically with your actual left hand. It cannot be done reliably in your head, and in an exam you can and should use your hand.

How a simple motor works

• A coil carrying a current sits in a magnetic field.
• The two sides of the coil carry current in opposite directions, so by the left-hand rule they experience forces in opposite directions — one up, one down.
• These two forces form a turning effect (a torque) that rotates the coil.
• A split-ring commutator reverses the current every half turn, so the forces keep pushing the coil the same way round instead of reversing.
• The turning effect is increased by: a stronger field, a larger current, more turns on the coil, or a larger coil area.