15.4 The Motor Effect

A free GCSE Physics lesson for AQA (8463) from OBA School: higher tier. The force on a current-carrying wire in a magnetic field, Fleming’s left-hand rule, F = B I l and the electric motor. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• (Higher tier) describe the motor effect and the factors that change the size of the force
• (Higher tier) use Fleming’s left-hand rule to find the direction of the force, current or field
• (Higher tier) recall that magnetic flux density B measures the strength of a field, in tesla
• (Higher tier) use F = B I l, including rearranging and converting units
• (Higher tier) explain how the force on a coil makes an electric motor rotate, and the job of the split-ring commutator

Key words

• Motor effect: A wire carrying a current in a magnetic field feels a force, because the field of the wire and the field of the magnet interact.
• Magnetic flux density (B): A measure of the strength of a magnetic field. Unit: tesla (T). 1 mT = 0.001 T.
• Fleming’s left-hand rule: A rule linking the directions of the field, the current and the force (motion), all at right angles.
• Split-ring commutator: Two half-rings connected to the ends of a motor coil. It reverses the current in the coil every half-turn.
• Brushes: Carbon (graphite) or metal contacts that press on the commutator and connect the spinning coil to the supply.

The motor effect

When a wire carrying a current is placed in a magnetic field, the magnetic field of the wire and the field of the magnet interact, and the wire feels a force. This is the motor effect. The magnet feels an equal and opposite force.

• The force is bigger if the current is bigger, the magnet is stronger, or a longer piece of wire is in the field.
• The force is reversed if either the current or the field is reversed. (Reversing both gives a force in the original direction.)
• The force is always at right angles to both the wire and the field.

Fleming’s left-hand rule

Hold the thumb and first two fingers of your left hand at right angles to each other:

Worked example: direction of the force

A horizontal wire runs from west to east with the current flowing east. The magnetic field points straight down.
First finger down (field), second finger east (current). The thumb then points north.

Answer: the force on the wire is towards the north

Exam tip: Use the left hand for the motor effect. A common mistake is to point the second finger the way electrons flow; it must point along the conventional current (+ to −).

Calculating the force: F = B I l

force = magnetic flux density × current × length

F = B I l

F in newtons (N), B in tesla (T), I in amperes (A), l in metres (m)

Rearranged: B = F ÷ (I l) I = F ÷ (B l) l = F ÷ (B I)

The equation applies when the wire is at right angles to the field, and l is the length of wire inside the field. Convert mT to T (÷ 1000) and mm or cm to m first.

Worked example: force on a wire

A wire carries 3.2 A at right angles to a field of 0.25 T. The length of wire in the field is 6.0 cm.
l = 6.0 cm = 0.060 m
F = B I l = 0.25 × 3.2 × 0.060

Answer: F = 0.048 N

Worked example: finding the flux density

A 40 mm length of wire in a field feels a force of 0.018 N when the current is 1.5 A.
l = 0.040 m; B = F ÷ (I l) = 0.018 ÷ (1.5 × 0.040) = 0.018 ÷ 0.060

Answer: B = 0.30 T

The electric motor

A simple d.c. motor has a rectangular coil of insulated wire on an axle between the poles of a magnet. The current flows in opposite directions along the two long sides of the coil, so the forces on them are in opposite directions: one side is pushed up and the other down. These two forces turn the coil.

After half a turn, the sides have swapped places. If the current kept the same direction, the forces would now push the coil back. The split-ring commutator stops this: it reverses the current in the coil every half-turn, so the side nearest the N-pole is always pushed the same way and the coil keeps spinning in one direction.

• spin faster; do this increase the current; use a stronger magnet; use more turns on the coil
• spin the other way; do this reverse the current (swap the battery connections) or reverse the magnet’s poles

Common mistakes

• Using the right hand. Fleming’s rule for the motor effect uses the left hand.
• Forgetting to convert mm or cm to m, or mT to T, before using F = B I l.
• Saying there is a force when the wire is parallel to the field. The force is then zero.
• Saying the commutator reverses the direction of rotation. It reverses the current in the coil so the rotation stays in the same direction.
• Saying that reversing both the current and the field reverses the force. Reversing both leaves the force unchanged.

Revision questions

Try these, then check your answers below each one.

Question 1. (Higher tier) What is the unit of magnetic flux density, B? (Choose from: tesla (T), newton (N), weber (Wb), ampere (A).)

Answer: tesla (T)

Working: Magnetic flux density is measured in tesla, T. 1 mT = 0.001 T.

Question 2. (Higher tier) A wire at right angles to a magnetic field of 40 mT carries a current of 2.5 A. The length of wire in the field is 60 mm. Calculate the force on the wire in newtons.

Answer: 0.006 N

Working: B = 0.040 T, l = 0.060 m. F = B I l = 0.040 × 2.5 × 0.060 = 0.0060 N.

Question 3. (Higher tier) A 10 cm length of wire at right angles to a 0.15 T field feels a force of 0.045 N. Calculate the current in the wire.

Answer: 3 A

Working: I = F ÷ (B l) = 0.045 ÷ (0.15 × 0.10) = 0.045 ÷ 0.015 = 3.0 A.

Related lessons

• Previous lesson: 15.3 Electromagnets in Devices
• Next lesson: 15.5 The Generator Effect
• In this chapter: 15.1 Magnetic Fields
• In this chapter: 15.2 Magnetic Fields of Electric Currents
• In this chapter: 15.6 The Alternating-Current Generator

Continue in the full course

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