Lenz’s Law: MDCAT Physics notes
Lenz’s Law MDCAT notes: direction of induced current, opposition to change in flux, conservation of energy, rings and magnets, and magnetic levitation.
Statement
Lenz's law: the direction of the induced current is always such that it opposes the change (in magnetic flux) that produces it.
Faraday's law gives the size of the induced emf; Lenz's law gives its direction. Together:
$$\varepsilon = -N\frac{\Delta\Phi}{\Delta t}$$
The negative sign is Lenz's law: the induced emf opposes the rate of change of magnetic flux. Lenz's law applies to the induced current and therefore to the induced emf driving it, including motional emf.
Conservation of energy
Lenz's law is a consequence of the law of conservation of energy. Suppose the induced current helped the change: pushing a magnet towards a coil would attract it further, accelerating it and producing more current with no work done, making energy from nothing. Because the induced current opposes the motion, we must do work to push the magnet, and that mechanical work appears as electrical energy (and heat) in the coil.
Applying the law
| Change | Induced current tries to | Mechanical effect |
|---|---|---|
| N pole moved towards a coil | Make the near face a N pole | Magnet is repelled; approach is opposed |
| N pole moved away from a coil | Make the near face a S pole | Magnet is attracted back; withdrawal is opposed |
| Current in a nearby coil increasing | Produce flux opposite to the rising flux | Ring is pushed away |
| Current in a nearby coil decreasing | Produce flux in the same direction to keep it up | Ring is pulled closer |
Key idea: an induced current opposes the change in flux, not the flux itself. If flux increases, the induced flux is opposite; if flux decreases, the induced flux is in the same direction.
Suspended ring
A metal ring hanging from a thread moves away when a magnet is brought towards it, and follows the magnet when it is pulled away. A ring with a cut in it has no induced current and does not move.
Loop moving towards a magnet
If a loop moves towards a stationary magnet, the relative motion is the same, so the induced current opposes the approach.
Applications
- Magnetic levitation (maglev) trains: induced currents in conducting coils or plates oppose the approaching magnets, giving a repulsive force that lifts the train. MDCAT keys this to Lenz's law.
- Eddy current braking and damping: induced currents in a moving metal plate oppose its motion.
- Back emf in motors: the emf induced in a spinning motor coil opposes the supply voltage.
Key formulas
- $\varepsilon = -N\,\Delta\Phi/\Delta t$ (minus sign = Lenz's law)
Common MDCAT traps
- Lenz's law gives direction; Faraday's law gives magnitude. Ohm's and Ampere's laws are distractors.
- Lenz's law is conservation of energy, not of charge, mass or momentum.
- The ring moves away from an approaching magnet, not towards it.
- The induced current opposes the change, not the existing field.
- Opposition is to change in magnetic flux, not electric flux.
Quick revision
- Induced current opposes the cause that produces it.
- Work done against the opposing force becomes electrical energy.
- Rising flux gives an opposing induced flux.
- Maglev trains are an application of Lenz's law.