Faraday's Law of Induction
Faraday's Law of Induction states that the electromotive force (EMF) induced in a closed loop is equal to the negative rate of change of magnetic flux through the loop. This fundamental law explains how changing magnetic fields produce electric currents, forming the basis of electric generators, transformers, and induction motors. It was discovered experimentally by Michael Faraday in 1831 and independently by Joseph Henry around the same time.
Key Formula
EMF = -N × (dΦ_B / dt)
LaTeX: \mathcal{E} = -N\frac{d\Phi_B}{dt}
| Symbol | Meaning | Unit |
|---|---|---|
| ℰ | Induced electromotive force (EMF) | Volt (V) |
| N | Number of turns in the coil | Dimensionless |
| dΦ_B/dt | Rate of change of magnetic flux | Weber per second (Wb/s) |
Worked Example
Problem
A coil of 200 turns is placed in a magnetic field. The magnetic flux through each turn changes uniformly from 0.05 Wb to 0.01 Wb in 0.4 seconds. Calculate the induced EMF.
Solution
Step 1: Identify the given values. N = 200 turns ΔΦ_B = 0.01 − 0.05 = −0.04 Wb Δt = 0.4 s Step 2: Apply Faraday's Law. ℰ = −N × (ΔΦ_B / Δt) ℰ = −200 × (−0.04 / 0.4) Step 3: Calculate the rate of flux change. ΔΦ_B / Δt = −0.04 / 0.4 = −0.1 Wb/s Step 4: Calculate EMF. ℰ = −200 × (−0.1) = +20 V
Answer
Induced EMF = 20 V (positive sign indicates direction via Lenz's Law)
Comparison of Faraday's Law Applications in Common Devices
| Device | Working Principle | Input | Output | Typical EMF |
|---|---|---|---|---|
| Electric Generator | Rotating coil in magnetic field | Mechanical energy | Electrical energy | 230 V (AC mains) |
| Transformer | Changing flux in primary coil | AC voltage | Different AC voltage | Varies by ratio |
| Induction Motor | Rotating magnetic field induces rotor current | AC supply | Mechanical torque | 415 V (3-phase) |
| Induction Cooktop | High-frequency flux in cooking vessel | AC supply | Heat in vessel | ~50 V induced |
| Microphone (dynamic) | Sound moves coil in magnetic field | Sound waves | Audio signal | mV range |
Interactive Tools
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Related Terms
Magnetic Flux
Magnetic flux is the total quantity of magnetic field lines passing perpendicularly through a given surface area, measuring how much of the magnetic field is captured by that surface. It is a scalar quantity defined as the dot product of the magnetic field vector and the area vector of the surface. Magnetic flux is fundamental to understanding electromagnetic induction, transformer operation, and the behaviour of inductors in circuits.
Lenz's Law
Lenz's Law states that the direction of an induced current is always such as to oppose the change in magnetic flux that caused it, thereby acting against the motion or change producing the induction. It is essentially a consequence of the conservation of energy and provides the negative sign in Faraday's Law of Induction. Named after Heinrich Lenz (1804–1865), the law explains why generators require mechanical work to produce electricity and underlies the principle of electromagnetic braking.
Electromagnetic Induction
Electromagnetic induction is the process by which a changing magnetic field within a closed conductor induces an electromotive force (EMF) and consequently an electric current in the conductor. Discovered by Michael Faraday in 1831, it is governed by Faraday's Law and Lenz's Law, and forms the operational basis of virtually all large-scale electrical power generation, transformers, and countless sensing devices. The phenomenon demonstrates the deep relationship between electricity and magnetism, first unified in Maxwell's equations.
Named after Michael Faraday (1791–1867), an English scientist who discovered electromagnetic induction in August 1831. "Induction" derives from Latin "inductio" meaning "a leading in or bringing forward".