Faraday’s law of induction states that the electromotive force induced in a circuit is proportional to the negative rate of change of magnetic flux through the circuit, EMF = −N × ΔΦ/Δt. The minus sign expresses Lenz’s law.
Learning objectives
- Define magnetic flux and explain its dependence on field, area and angle.
- Apply Faraday’s law to calculate an induced EMF.
- Calculate motional EMF for a conductor moving in a magnetic field.
- Explain the role of the law in generators and transformers.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
This is how a bicycle dynamo, a power-station generator and a transformer work. In a generator, a coil rotates in a magnetic field, so the flux through it keeps changing and an alternating voltage is produced. In a transformer, the changing flux in the core links a second coil and induces a voltage there.
Intermediate How it behaves in a circuit
For a straight conductor of length l moving with velocity v perpendicular to a uniform field B, the motional EMF is EMF = B × l × v. The same law explains why a changing current in one coil induces a voltage in a nearby coil: the changing current produces a changing magnetic flux, which links the second coil. The induced EMF opposes the change that produced it, as described by Lenz’s law.
Advanced Limits, assumptions, engineering detail
In real machines and transformers, flux is not perfectly confined, winding resistance and leakage inductance matter, and core losses appear as hysteresis and eddy currents. At high frequency, skin and proximity effects redistribute current in the conductors. The ideal law still sets the fundamental relationship between voltage, turns and flux rate, which is why transformer voltage ratio follows the turns ratio and why generator voltage rises with speed and field strength.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Magnetic flux | Φ | weber (Wb) |
| Magnetic flux density | B | tesla (T) |
| Induced EMF | EMF | volt (V) |
| Number of turns | N | dimensionless |
Worked examples
EMF from a changing flux
Problem. A coil of 200 turns experiences a flux change of 0.0040 Wb in 0.020 s. Find the induced EMF.
Solution. EMF = N × ΔΦ/Δt = 200 × 0.0040 / 0.020 = 200 × 0.20 = 40 V.
Motional EMF in a moving conductor
Problem. A 0.40 m conductor moves at 10 m/s perpendicular to a 0.50 T field. What EMF is induced?
Solution. EMF = B × l × v = 0.50 T × 0.40 m × 10 m/s = 2.0 V.
Practical applications
- Generators and alternators
- Transformers and inductive charging
- Magnetic sensors and tachometers
- Induction heating and braking
Automotive applications
An alternator uses a rotating magnetic field to induce an alternating voltage in stator windings. The voltage rises with rotor speed and field current, and the regulator controls the field so that the system voltage stays within limits. Ignition coils also rely on induction: the primary current is interrupted, the flux collapses quickly, and the resulting high EMF in the secondary winding fires the spark plug.
Industrial applications
Transformers in industrial distribution step voltage up or down by magnetic induction. Their voltage ratio follows the turns ratio, but real transformers have losses, leakage flux and temperature limits. Induction motors use the same principle in reverse: a rotating field induces currents in the rotor, which produce torque. Induction heating uses eddy currents to heat conductive materials without contact.
Measurement procedure
- Measure the induced voltage with a voltmeter or oscilloscope; the reading depends on the flux change rate and the meter loading.
- To measure a coil’s induced EMF, keep the circuit open or use a high-impedance instrument so the current does not distort the result.
- For rotating machines, use an oscilloscope to see the waveform, frequency and amplitude rather than a single average value.
- Verify the magnetic polarity of windings before connecting them, because the induced voltage direction follows Lenz’s law.
Common mistakes
- Forgetting the number of turns when calculating the EMF of a coil.
- Using the flux itself instead of the rate of change of flux.
- Ignoring the angle between the field and the area: Φ = BA only when the field is perpendicular to the area.
- Assuming an induced EMF requires a closed circuit; the EMF exists even when the circuit is open, although current does not flow.
Safety considerations
- Induced EMFs can be very high when current in an inductive circuit is interrupted; use appropriate suppression and do not open inductive circuits by hand.
- Rotating machines and transformers store energy in their magnetic fields; follow lockout and discharge procedures before working on them.
- High-voltage induction systems can cause serious injury; keep clear of exposed windings and terminals.