Faraday's Law of Induction
A changing magnetic flux induces an electromotive force.
Formula
Variables
Example
Moving a magnet through a coil induces a voltage — the basis of every generator.
How it works
Faraday's law says that an emf appears only when the magnetic flux through a circuit changes, and the minus sign tells you the induced emf acts to oppose that change. In practice, the flux can change because the magnetic field gets stronger or weaker, the loop's area changes, or the loop rotates in the field. This is a direct consequence of how electric and magnetic fields are coupled: a time-varying magnetic environment creates a circulating electric field that pushes charges around the loop.
When to use it
Use this law whenever a magnetic field or a conducting loop is changing in time, such as in generators, transformers, inductors, wireless charging, and eddy-current problems. It is also the starting point for finding induced voltages in any closed circuit when flux changes are given or can be inferred.
Worked example, step by step
A 20-turn coil has its magnetic flux per turn reduced uniformly from 5.0×10^-3 Wb to 1.0×10^-3 Wb in 0.040 s. Step 1: Find the change in flux per turn: ΔΦ_B = 1.0×10^-3 - 5.0×10^-3 = -4.0×10^-3 Wb. Step 2: Use Faraday's law for N turns: ε = -N(ΔΦ_B/Δt). Step 3: Substitute values: ε = -20[(-4.0×10^-3 Wb)/(0.040 s)]. Step 4: Compute: ε = -20(-0.10 V) = 2.0 V. Final answer: The induced emf has magnitude 2.0 V, with polarity that opposes the decrease in flux.
Common mistakes to avoid
- Ignoring the minus sign and losing the direction/polarity of the induced emf
- Using the magnetic field B instead of magnetic flux Φ_B, which also depends on area and orientation
- Forgetting the number of turns N in a coil, which multiplies the induced emf
Did You Know?
Faraday's discovery of induction is why every power plant on Earth generates electricity by spinning magnets.
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