Electromagnetic Induction
Reference for Faraday's law and Lenz's law.
Calculate induced EMF from changing magnetic flux with worked examples.
Covers flux linkage and solenoids.
The Formula
Faraday's Law: EMF = -N × ΔΦ / Δt
Magnetic Flux: Φ = B × A × cos(θ)
Magnetic Flux: Φ = B × A × cos(θ)
Faraday's law states that a changing magnetic flux through a coil induces an electromotive force (voltage). The negative sign (Lenz's law) indicates the induced EMF opposes the change that produced it.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| EMF | Induced electromotive force | Volts (V) |
| N | Number of turns in the coil | (unitless) |
| ΔΦ | Change in magnetic flux | Weber (Wb) |
| Δt | Time over which the change occurs | Seconds (s) |
| B | Magnetic field strength | Tesla (T) |
| A | Area of the coil | m² |
| θ | Angle between B and the normal to the coil | degrees or radians |
Example 1
A 50-turn coil has its flux change from 0.02 Wb to 0 in 0.1 seconds
ΔΦ = 0 - 0.02 = -0.02 Wb
EMF = -N × ΔΦ / Δt = -50 × (-0.02) / 0.1
= 10 V
Example 2
Find the flux through a 0.05 m² coil in a 0.3 T field at 60°
Φ = B × A × cos(θ) = 0.3 × 0.05 × cos(60°)
= 0.3 × 0.05 × 0.5
= 0.0075 Wb
When to Use It
Use electromagnetic induction when:
- Designing electric generators and alternators
- Understanding how transformers work
- Analyzing inductors in circuits
- Studying wireless charging, induction cooking, and electromagnetic braking
Key Notes
- Faraday's law: EMF = −dΦ/dt: The induced EMF equals the negative rate of change of magnetic flux. The negative sign (Lenz's law) means the induced current opposes the change that caused it — a consequence of energy conservation.
- Magnetic flux: Φ = B · A · cosθ: Flux depends on field strength (B), the area of the loop (A), and the angle between B and the normal to the loop. Maximum flux when B is perpendicular to the loop plane (θ = 0°).
- Three ways to change flux: Induction occurs when (1) the magnetic field strength changes, (2) the area of the loop changes (moving conductor), or (3) the angle between B and the loop changes (rotating generator). Generators use all three.
- Lenz's law gives the direction: The induced current always flows in a direction that creates a magnetic field opposing the change in flux. This is why it takes effort to pull a magnet out of a coil — the induced current resists the motion.
- Engineering applications: Faraday's law is the operating principle behind electric generators, transformers, induction cooktops, wireless phone chargers (Qi), and metal detectors.