Magnetism and the Motor Effect
The motor effect is the force produced on a current-carrying conductor when it is placed inside a magnetic field, and it is the working principle behind electric motors and loudspeakers. When a wire carrying a current is at right angles to the field, the force is at its maximum and can be calculated using force = magnetic flux density x current x length (F = B I L), with its direction predicted using Fleming's left-hand rule.
Method
- Identify the three things needed for the motor effect: a magnetic field (from a permanent magnet or an electromagnet), a conductor carrying a current, and the conductor placed inside that field so it is not parallel to the field lines.
- Learn the equation for the force when the conductor is at right angles to the field: force (N) = magnetic flux density (T) x current (A) x length (m), or F = B I L. This is the maximum possible force for given values of B, I and L; if the wire is parallel to the field, there is no force at all.
- Rearrange F = B I L using the triangle method to find B, I or L when the question asks for one of those instead of F, and always convert any length given in cm into metres before substituting.
- Use Fleming's left-hand rule to find the direction of the force: point the First finger in the direction of the Field (from north to south), the SeCond finger in the direction of the Current (conventional current, from positive to negative), and the Thumb then points in the direction of the force (Thrust).
- For a current-carrying coil rather than a single straight wire, apply the same rule to each side of the coil separately: because the current flows in opposite directions along the two long sides of the coil, the forces on the two sides point in opposite directions, and this pair of forces creates a turning effect that rotates the coil.
- For d.c. electric motor questions, describe the role of the split-ring commutator: it reverses the direction of the current in the coil every half turn, which reverses the direction of the force on each side of the coil at the same point, keeping the coil turning continuously in the same direction rather than oscillating back and forth.
- To make a motor turn with a greater force, link the answer back to the equation and the field: increase the current, use a stronger magnetic field, or add more turns to the coil, since each turn adds to the total force.
Worked example
A straight wire of length 0.40 m carries a current of 3.0 A. The wire is at right angles to a magnetic field of flux density 0.25 T. Calculate the force on the wire.
- Write down the equation: force = magnetic flux density x current x length (F = B I L).
- Check the units are correct: B in tesla, I in amps, L in metres (all already correct here).
- Substitute the values: F = 0.25 x 3.0 x 0.40.
- Calculate in two steps: 0.25 x 3.0 = 0.75, then 0.75 x 0.40 = 0.30.
- Final answer: the force on the wire is 0.30 N, and since the wire is at right angles to the field, this is the maximum possible force for these values of B, I and L.
Practice questions
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Q1State the three factors needed for a current-carrying wire to experience a force due to the motor effect.Show answer
Answer: A magnetic field, a current flowing through the wire, and the wire must not be parallel to the magnetic field (it must have a component at right angles to the field).
Q2A wire of length 0.20 m carries a current of 5.0 A at right angles to a magnetic field of flux density 0.60 T. Calculate the force on the wire.Show answer
Answer: 0.60 N (F = B I L = 0.60 x 5.0 x 0.20 = 0.60 N)
Q3A current-carrying wire experiences a force of 1.2 N when placed at right angles to a magnetic field of flux density 0.40 T, carrying a current of 6.0 A. Calculate the length of wire in the field.Show answer
Answer: 0.50 m (L = F / (B x I) = 1.2 / (0.40 x 6.0) = 1.2/2.4 = 0.50 m)
Q4State the name of the rule used to find the direction of the force on a current-carrying wire in a magnetic field, and name the three quantities it relates.Show answer
Answer: Fleming's left-hand rule; it relates the direction of the magnetic Field, the direction of the Current, and the direction of the resulting force (Thrust).
Q5In a simple d.c. electric motor, state the name and function of the component that reverses the current in the coil every half turn.Show answer
Answer: The split-ring commutator; it reverses the direction of the current in the coil every half turn so the forces on the coil keep turning it in the same direction, producing continuous rotation.
Q6State two ways of increasing the force produced by a motor effect setup, for a wire of fixed length at a fixed angle to the field.Show answer
Answer: Increase the current through the wire, or increase the magnetic flux density (use a stronger magnet).
Q7Explain why a current-carrying wire positioned exactly parallel to a magnetic field experiences no force.Show answer
Answer: The motor effect force only occurs when the current has a component at right angles to the field; when the wire is parallel to the field there is no component at right angles to it, so no force acts.
Q8A rectangular coil carrying a current is placed in a magnetic field, with its two long sides parallel to each other. Explain why the coil rotates rather than moving in a straight line.Show answer
Answer: The current flows in opposite directions along the two long sides of the coil, so in the same magnetic field the forces on the two sides act in opposite directions; this pair of opposite forces produces a turning effect, which rotates the coil rather than pushing it in a straight line.
Exam-style questions
Written in the style of a GCSE Science exam paper, with a full mark scheme.
A straight copper wire of length 0.15 m is placed at right angles inside a uniform magnetic field of flux density 0.80 T. When a current is passed through the wire, it experiences a force of 0.36 N. Calculate the size of the current in the wire.
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Describe how a student would use Fleming's left-hand rule to work out the direction of the force on a current-carrying wire in a magnetic field, once the directions of the field and the current are known.
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A simple direct current (d.c.) electric motor consists of a rectangular coil of wire that can rotate between the poles of a permanent magnet, connected to a battery through a split-ring commutator and brushes. Explain how this motor produces continuous rotation, referring to the forces on the coil and the role of the split-ring commutator.
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