Faraday's Law and Lenz's Law
Simple Explanation
Faraday's law states that a changing magnetic flux induces an EMF, epsilon=-N(DeltaPhi/Deltat) β and Lenz's law (the negative sign) says that induced EMF always drives a current that OPPOSES the change in flux that created it.
Why Do We Need It?
This is the single most important law in this chapter β it is the physics behind every electric generator (and, in reverse, every electric motor) in the world.
See It
A bar magnet with north and south poles moving toward a coil of wire (shown as three loops), with an arrow indicating the induced current direction in the coil
Formula
Faraday's Law of Electromagnetic Induction
Ξ΅ = βN(ΞΞ¦/Ξt)
A changing magnetic flux through a coil induces an EMF, proportional to how fast the flux changes and to the number of turns in the coil β the negative sign (Lenz's law) shows the induced EMF always opposes the change that created it.
- Ξ΅
- β induced EMF, in volts (V)
- N
- β number of turns (loops) in the coil
- ΞΞ¦
- β change in magnetic flux through one turn, in webers (Wb)
- Ξt
- β time over which the flux changes, in seconds (s)
When to use it: Whenever the EMF induced by a changing magnetic flux through a coil needs to be found.
Worked Example
Find an induced EMF
A coil of 100 turns experiences a change in magnetic flux of 0.02 Wb over 0.5 seconds. Find the magnitude of the induced EMF.
Why Does This Work?
More turns (N) means the same changing flux threads through more loops of wire, each contributing its own share of induced EMF, so the total EMF scales directly with N β and a faster-changing flux (smaller Deltat for the same DeltaPhi) induces a proportionally larger EMF, exactly as the formula shows.
Real-Life Example
A bicycle dynamo lighting a lamp
A bicycle dynamo generates electricity to power a lamp, using the wheel's rotation to spin a magnet near a coil.
The spinning magnet continuously changes the magnetic flux through the coil, inducing an EMF exactly as Faraday's law describes β pedaling faster changes the flux more quickly, producing a brighter light.
Practice
A coil of 200 turns experiences a flux change of 0.01 Wb over 0.2 seconds. Find the magnitude of the induced EMF.
HardCommon mistake
Forgetting Lenz's law's directional meaning β the induced current does not simply flow in whatever direction is convenient; it always flows in the direction that OPPOSES the change in flux, which is essential for correctly predicting current direction in any induction problem.
Quick Review
- epsilon = -N(DeltaPhi/Deltat).
- Lenz's law: induced current always opposes the change that created it.
- The physics behind every electric generator.