Faraday's Law of Induction
Faraday's law EMF = -dPhi/dt calculates induced voltage from changing magnetic flux.
Learn electromagnetic induction with examples.
The Formula
Faraday's law states that a changing magnetic flux through a loop of wire induces an electromotive force (voltage). The negative sign indicates that the induced EMF opposes the change in flux, consistent with Lenz's law.
Michael Faraday discovered electromagnetic induction in 1831 in England. This discovery is the foundation of all electric generators, transformers, and inductors. Without it, modern electrical power generation would not exist.
The magnetic flux Φ through a loop equals B × A × cos(θ), where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the field and the normal to the loop. Flux can change by varying B, A, or the angle θ. For N loops of wire, the total EMF is multiplied by N.
Variables
| Symbol | Meaning |
|---|---|
| EMF | Induced electromotive force (volts, V) |
| N | Number of turns in the coil |
| ΔΦ | Change in magnetic flux (weber, Wb) |
| Δt | Time interval for the change (seconds, s) |
Example 1
A coil with 200 turns experiences a flux change from 0.05 Wb to 0.02 Wb in 0.1 seconds. What is the induced EMF?
Calculate flux change: ΔΦ = 0.02 − 0.05 = −0.03 Wb
Apply the formula: EMF = −N × ΔΦ/Δt = −200 × (−0.03)/0.1
EMF = −200 × (−0.3) = 60
EMF = 60 V
Example 2
A single loop of wire with area 0.04 m² is in a magnetic field that increases uniformly from 0 to 1.5 T in 0.5 seconds. What EMF is induced?
Flux change: ΔΦ = B × A = 1.5 × 0.04 = 0.06 Wb (from 0 Wb initially)
EMF = −N × ΔΦ/Δt = −1 × 0.06/0.5
EMF = −0.12 V (magnitude: 0.12 V)
When to Use It
Use Faraday's law whenever a changing magnetic field induces a voltage in a conductor.
- Calculating the output voltage of electric generators
- Designing transformers for voltage conversion
- Understanding how induction cooktops and wireless chargers work
- Analyzing eddy currents in conducting materials