Electromagnetic induction: Faraday's and Lenz's laws

Induction by motion

Moving a magnet into or out of a coil, or moving a wire through a field, induces an e.m.f. The e.m.f. is larger if:

• the relative motion is faster
• the field is stronger
• the coil has more turns (and larger area)

No motion, no change in flux linkage, no e.m.f.

Induction by a changing current

A changing current in one coil makes a changing field that links a second coil, inducing an e.m.f. in it. The e.m.f. is larger if the current changes faster, the coils have more turns, or an iron core links them. A steady d.c. current induces nothing, which is why transformers need a.c.

Faraday's and Lenz's laws

• Faraday's law: the induced e.m.f. is proportional to the rate of change of flux linkage.
• Lenz's law: the direction of the induced e.m.f. (and current) is such as to oppose the change that causes it.

Together: ε = -N dφ/dt. The minus sign is Lenz's law. For an average e.m.f., use ε = NΔφ / Δt.

Lenz's law and energy

If you push a magnet into a coil, the induced current makes the coil repel the magnet, so you must do work. That work becomes electrical energy. If the induced current helped the motion, energy would be created from nothing. For a straight conductor of length l moving at v perpendicular to B, ε = Blv.

Worked example

A 500-turn coil of area 4.0 x 10^-3 m² is perpendicular to a 0.20 T field. The field falls to zero in 0.050 s. Find the average induced e.m.f.

1. Change in flux linkage = NBA = 500 x 0.20 x 4.0 x 10^-3 = 0.40 Wb turns
2. ε = 0.40 / 0.050

Answer: ε = 8.0 V

Check yourself

1. The flux through a 200-turn coil changes by 3.0 x 10^-4 Wb in 0.020 s. Find the average e.m.f. in V.
   Show answer

   3 V. ε = NΔφ / Δt = 200 x 3.0 x 10^-4 / 0.020 = 3.0 V.

2. A 0.50 m rod moves at 4.0 m/s at right angles to a 0.30 T field. Find the induced e.m.f. in V.
   Show answer

   0.6 V. ε = Blv = 0.30 x 0.50 x 4.0 = 0.60 V.

3. A 150-turn coil of area 2.0 x 10^-3 m² is turned from perpendicular to parallel to a 0.50 T field in 0.10 s. Find the average e.m.f. in V.
   Show answer

   1.5 V. Δ(Nφ) = 150 x 0.50 x 2.0 x 10^-3 = 0.15 Wb turns; ε = 0.15 / 0.10 = 1.5 V.

4. What does Lenz's law state?
   • The induced e.m.f. equals the rate of change of flux linkage
   • The induced e.m.f. acts to oppose the change that causes it
   • The induced current always flows clockwise
   • The induced e.m.f. is proportional to the number of turns only
   Show answer

   The induced e.m.f. acts to oppose the change that causes it. Lenz's law gives the direction; Faraday's law gives the size.

5. What does the minus sign in ε = -N dφ/dt represent?
   • That the e.m.f. is always negative
   • That flux decreases with time
   • The resistance of the coil
   • Lenz's law
   Show answer

   Lenz's law. It shows the induced e.m.f. opposes the change in flux linkage.

6. A magnet is pushed into a coil connected to a voltmeter. Which change would increase the reading?
   • Using a coil with fewer turns
   • Pushing the magnet in faster
   • Using a weaker magnet
   • Holding the magnet still inside the coil
   Show answer

   Pushing the magnet in faster. A faster motion gives a faster rate of change of flux linkage.

7. A steady direct current flows in a primary coil wound on an iron core. What e.m.f. is induced in a secondary coil on the same core?
   • A steady e.m.f.
   • An alternating e.m.f.
   • An e.m.f. equal to the primary p.d.
   • None, because the flux linkage is not changing
   Show answer

   None, because the flux linkage is not changing. Induction needs a changing flux linkage; a steady current gives a constant flux.

8. A magnet falls more slowly through a copper tube than through a plastic one. Why?
   • Copper is magnetic and attracts the magnet
   • Air resistance is greater in copper tubes
   • Induced currents in the copper produce a field that opposes the magnet's motion
   • The copper tube is heavier
   Show answer

   Induced currents in the copper produce a field that opposes the magnet's motion. By Lenz's law, the induced currents oppose the change, slowing the magnet.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Pearson Edexcel IAL Physics Unit 4 (WPH14) question paper, June 2024: list of data, formulae and relationships

Last updated 7 November 2026. Spotted a mistake? Tell us.