Formula & Calculator
Faraday's Law of Electromagnetic Induction
Calculates the electromotive force induced in a coil from the rate of change of magnetic flux through it and the number of turns.
Interpretation
Faraday's law: EMF = –N·(ΔΦ/Δt), where N is number of turns, ΔΦ is change in magnetic flux, Δt is time. It describes induced EMF due to changing flux. Example: N=100, ΔΦ=0.01 Wb in 0.1 s → EMF = –100×0.01/0.1 = –10 V.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| EMF | Induced electromotive force | V |
| N | Number of turns in the coil | |
| delta_Phi | Change in magnetic flux | Wb |
| delta_t | Time interval over which the flux changes | s |
What it means
Faraday’s law of induction states that the induced electromotive force (EMF) in a closed circuit is equal to the negative of the time rate of change of magnetic flux through the circuit. The negative sign (Lenz’s law) indicates that the induced current opposes the change in flux. This law is fundamental to the operation of electrical generators, transformers, and motors. It also explains eddy currents and induction heating. In engineering, it is used to design magnetic sensors, inductors, and wireless power transfer systems. The law is also applied in electromagnetic braking and in measuring magnetic fields. Understanding Faraday’s law is essential for all of electrical engineering and many areas of applied physics.
Worked example
Faraday's Law – Two Examples
Real‑World| Parameter | Value |
|---|---|
| N | 100 |
| ΔΦ | 0.01 Wb |
| Δt | 0.5 s |
| Parameter | Value |
|---|---|
| N | 50 |
| ΔΦ | 0.02 Wb |
| Δt | 0.1 s |
Common mistakes
- Sign convention: The negative sign (Lenz’s law) indicates the induced EMF opposes the change in flux – do not drop it.
- Number of turns N: For a coil – if N=1, use 1.
- Change in flux ΔΦ: Final flux minus initial flux – can be negative.
- Time interval Δt: In seconds – EMF in volts.
- Induced EMF: It is generated only when flux changes; constant flux gives zero EMF.
Applications
Faraday's law of electromagnetic induction, EMF = −N·ΔΦ/Δt, is the basis for generating electricity in power plants, as well as for transformers, induction motors, and wireless charging. It states that a changing magnetic flux induces an electromotive force (EMF) in a coil. Engineers use this law to design alternators, generators, and motors, to optimise efficiency, and to analyse electromagnetic interference. In automotive applications, it is used in anti‑lock braking sensors. In renewable energy, it is central to wind turbine generators and hydroelectric systems. By applying Faraday's law, professionals can harness and control electromagnetic energy for myriad applications.
- Design of electrical generators and alternators
- Transformer design for power distribution
- Induction motor and linear motor design
- Wireless power transfer and inductive charging
- Electromagnetic flow meters and sensors
Frequently Asked Questions
Faraday's law states that the induced electromotive force (EMF) in a closed circuit is proportional to the negative rate of change of the magnetic flux through the circuit: EMF = –N·dΦ/dt, where N is the number of turns.
The negative sign represents Lenz's law: the induced current flows in a direction that opposes the change in flux. This is a consequence of conservation of energy.
Dropping or misapplying the negative sign, or forgetting that the flux must be changing (not just present) to induce an EMF. If the flux is constant, the EMF is zero.
The EMF is measured in volts (V).
In a generator, a coil rotates in a magnetic field, causing a sinusoidal change in flux. The induced EMF is proportional to the rate of change of flux, leading to alternating current (AC).
- Motional EMF arises from the movement of a conductor in a magnetic field (e.g., moving rod).
- Transformer EMF arises from a changing magnetic field (e.g., in a transformer).
The induced current creates a magnetic field that opposes the change in the original flux. If the flux is increasing, the induced field opposes it; if decreasing, it tries to maintain it.
Lenz's law ensures that the induced current does work against the force that changed the flux, conserving energy. If the induced current aided the change, it would create a runaway effect (perpetual motion).