Faraday's Law of Induction
When the magnetic field passing through a loop of wire changes, it creates a voltage in that loop — even with no battery attached. Change the field faster, and you get a bigger voltage; this is exactly how generators turn motion into electricity.
The formula
ε = −ΔΦ / Δt
- ε — induced emf (V): the voltage created in the loop
- Φ — magnetic flux (Wb): the amount of magnetic field passing through the loop
- t — time (s): how long the change in flux takes
Worked example
The magnetic flux through a loop drops by 6 webers over 3 seconds. What voltage does this induce?
- ΔΦ = 6 Wb
- Δt = 3 s
- ε = −ΔΦ / Δt
- ε = −(6 Wb) / (3 s)
ε = −2 V
Test yourself
The flux still changes by 6 webers, but now it happens in just 2 seconds instead of 3. What is the size of the induced voltage now?
- 2 V
- Correct answer: 3 V
- 12 V
Right! A faster change means more voltage: 6 Wb ÷ 2 s = 3 V.
According to Lenz's law, the current induced by a changing flux will create its own magnetic field that…
- Correct answer: opposes the change in flux
- matches the change in flux
- has no effect on the flux
Exactly — the induced current always fights back against the change that created it, which is why the formula has a minus sign.
Where you see this
Every power plant on Earth is this law at industrial scale: spinning magnets sweep changing flux through coils, and out comes the voltage that reaches your wall socket. A bicycle dynamo is the pocket edition — your pedaling spins a magnet, and the headlight glows with no battery in the circuit.
Common mistakes
The essential point is change: a huge, perfectly steady magnetic field through a loop induces nothing — only a changing flux produces a voltage, ε = −ΔΦ / Δt. Then it's a rate, not an amount: the same 6 Wb change done in 2 s instead of 3 s raises the voltage from 2 V to 3 V. And the minus sign is Lenz's law — the induced current always opposes the change that created it, refusing a free lunch.
How it connects
This completes the pair the Lorentz force began: fields push charges, and now changing fields create the voltages that set charges moving — no battery required. Lenz's opposing push is energy conservation speaking, and AC resonance, next, is what happens when this induced voltage meets a capacitor in a circuit driven back and forth.