Every time you charge your phone, drive a car, or switch on a light, you are using a technology built on a discovery made in 1831 by Michael Faraday: electromagnetic induction. Faraday found that a changing magnetic field through a conductor induces a voltage — and that this induced voltage drives a current. This single insight enabled the invention of generators, transformers, and electric motors, and remains the basis of virtually all electrical power generation on Earth today.
The induced EMF in a circuit is equal to the negative rate of change of magnetic flux through the circuit:
EMF = −dΦ/dt
For a coil of N turns: EMF = −N dΦ/dt
where Φ = BA cosθ is magnetic flux (Wb), B is flux density (T), A is the area (m²), and θ is the angle between B and the normal to the coil. The negative sign embodies Lenz's Law.
Magnetic Flux and Why Change Matters
Magnetic flux Φ = BA cosθ measures how much magnetic field passes through a loop. A static flux — no matter how large — induces no EMF. Only a changing flux induces an EMF. The flux can change because:
• B changes in magnitude (e.g. a magnet moving toward a coil)
• The area A changes (e.g. a coil being stretched)
• The angle θ changes (e.g. a coil rotating in a fixed field — the basis of generators)
Lenz's Law: The Direction of Induced Current
The negative sign in Faraday's law encodes Lenz's Law: the induced current flows in a direction such that its magnetic effect opposes the change in flux that caused it.
Practical rule: push a north pole into a coil → the induced current creates a north pole facing the approaching magnet (opposing the increase in flux). Pull the magnet away → the induced current creates a south pole, trying to maintain the flux as it decreases.
Lenz's Law is conservation of energy in action. If the induced current aided the flux change rather than opposing it, you could get a self-amplifying current from nothing — violating the first law of thermodynamics. The opposing force Lenz's Law creates is why generators require mechanical work to rotate against the magnetic braking effect.
EMF = N dΦ/dt — more turns N does increase EMF for the same rate of flux change. But the flux change matters as much as N. A coil rotating slowly in a strong field may induce less EMF than a coil rotating fast in a weaker field. Both N and dΦ/dt determine the output.
Worked Examples
Example 1: Flux change through a coil
A 200-turn coil of area 0.05 m² is in a uniform magnetic field. B increases from 0.2 T to 0.8 T in 0.4 s. Find the induced EMF.
Example 2: Rotating coil (generator)
A 100-turn coil of area 0.02 m² rotates at 50 Hz in a 0.3 T field. Find the peak EMF.
The instantaneous EMF varies sinusoidally: EMF(t) = 188.5 sin(2π × 50 × t) — this is how AC generators produce sinusoidal alternating current.
Generators: Mechanical Energy → Electrical Energy
An AC generator (alternator) converts mechanical rotation to electrical energy using electromagnetic induction. A coil rotates in a magnetic field — the angle θ between the coil normal and B changes continuously, so flux Φ = BA cosθ changes continuously, inducing a sinusoidal EMF.
In a power station, the mechanical rotation is provided by steam turbines (coal, gas, nuclear) or water turbines (hydroelectric) or wind (wind turbines). The rotating coil is the rotor; the stationary magnets or field coils form the stator. Slip rings (not a commutator) maintain continuous contact, allowing AC output.
In the UK, generators produce 50 Hz AC at ~25,000 V, which is stepped up to 275,000–400,000 V by transformers for transmission, then stepped back down for domestic use at 230 V.
Transformers: Changing Voltage Using Induction
A transformer uses mutual induction to change AC voltage. An alternating current in the primary coil (N_p turns) creates a changing magnetic flux in a soft iron core. This changing flux passes through the secondary coil (N_s turns), inducing an EMF in it.
For an ideal transformer, power is conserved: V_p I_p = V_s I_s. So:
A step-up transformer (N_s > N_p) increases voltage and decreases current. A step-down transformer (N_s < N_p) decreases voltage and increases current. National grids use step-up transformers to reduce transmission current — since power losses in cables are P_loss = I²R, reducing current dramatically reduces waste heat.
| Device | Principle | Energy conversion |
|---|---|---|
| Generator / alternator | Rotating coil in B field | Mechanical → electrical |
| Transformer | Mutual induction via iron core | AC voltage change (same frequency) |
| Electric motor | Force on current in B field | Electrical → mechanical |
| Induction charging | Mutual induction (no contact) | AC electrical → AC electrical (wireless) |
Self-Inductance and Inductors
When the current in a coil changes, the changing magnetic flux the coil itself creates induces an EMF in the same coil — opposing the change in current. This is self-inductance:
where L is the inductance (henries, H). An inductor opposes changes in current — it resists sudden increases or decreases, smoothing current flow. Inductors are used in power supplies to filter ripple, in tuned LC circuits (radios, TVs) to select frequencies, and in transformers.
Frequently Asked Questions
What is electromagnetic induction?
Electromagnetic induction is the production of an EMF (and hence a current, if the circuit is closed) by a changing magnetic flux through a conductor. Discovered by Michael Faraday in 1831. Described by Faraday's law: EMF = −N dΦ/dt. It is the basis of generators, transformers, and wireless charging.
What is Faraday's law?
Faraday's law states that the induced EMF equals the negative rate of change of magnetic flux: EMF = −N dΦ/dt. The negative sign (Lenz's law) means the induced current opposes the flux change. Larger N (more turns) or faster flux change gives larger EMF.
What is Lenz's law?
Lenz's law states that the induced current always flows in a direction to oppose the change in magnetic flux that caused it. It is a consequence of energy conservation — if the induced current aided the flux change, a self-amplifying current would violate the first law of thermodynamics. Lenz's law gives the negative sign in Faraday's law.
How does a generator work?
A generator rotates a coil in a magnetic field. The changing angle between the coil and field produces a sinusoidally varying flux, inducing a sinusoidal AC EMF: EMF = NBAω sin(ωt). Mechanical energy (from steam, water, or wind) drives the rotation; electrical energy is extracted. Peak EMF = NBAω.
How does a transformer work?
A transformer uses mutual induction. An AC current in the primary coil creates a changing flux in an iron core. This changing flux passes through the secondary coil, inducing an EMF proportional to the turns ratio: V_s/V_p = N_s/N_p. Step-up transformers increase voltage (and decrease current); step-down do the reverse. Transformers only work with AC — not DC.
Why do transformers only work with AC?
Transformers require a changing magnetic flux to induce an EMF. DC current creates a constant (non-changing) flux, inducing zero EMF in the secondary. AC current continuously changes, creating continuously changing flux, continuously inducing an EMF in the secondary. A DC source connected to a transformer primary simply produces a constant magnetic field — no output.
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Written by
Dr. Sarah KimThermodynamics researcher with a PhD from MIT, specializing in statistical mechanics and energy transfer. Passionate about connecting molecular physics to everyday phenomena.
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