Faraday Law of Induction
A changing magnetic flux induces an EMF.
Formula
Variables
Example
Basis of generators
How it works
Faraday’s law says that if the magnetic flux through a loop changes, an electromotive force (EMF) appears around the loop. The negative sign is Lenz’s law: the induced EMF drives a current whose magnetic effect opposes the change in flux, which is required by conservation of energy. In practice, the flux can change because the magnetic field strength changes, the loop area changes, or the loop rotates relative to the field.
When to use it
Use this when a problem involves a coil, loop, solenoid, transformer, or any situation where magnetic flux through a circuit is changing. It is especially useful for finding induced voltages in moving conductors, rotating coils, and time-varying magnetic fields.
Worked example, step by step
A single circular loop experiences a magnetic flux that decreases from 0.080 Wb to 0.020 Wb in 0.15 s. Step 1: Write the change in flux: ΔΦ_B = 0.020 - 0.080 = -0.060 Wb Step 2: Use Faraday’s law for the average induced EMF: ε = -ΔΦ_B/Δt Step 3: Substitute the values: ε = -(-0.060)/0.15 Step 4: Compute: ε = 0.40 V Final answer: the magnitude of the induced EMF is 0.40 V, and its direction is such that it opposes the decrease in magnetic flux.
Common mistakes to avoid
- Forgetting the minus sign and ignoring the direction set by Lenz’s law
- Using magnetic field B directly instead of magnetic flux Φ_B = BA cosθ
- Mixing up flux change over time with the instantaneous value of flux
Did You Know?
Faraday's law of induction is the principle behind every electric generator and transformer on the grid.
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