Lenz's Law
Induced current opposes the change in flux that produced it.
Formula
Variables
Example
A magnet dropped through a copper tube falls slowly — induced currents oppose its motion.
How it works
Lenz’s law gives the direction of an induced emf: when the magnetic flux through a circuit changes, the induced current creates its own magnetic field that opposes that change. The minus sign in varepsilon \propto -\frac{d\Phi_B}{dt} is a compact way of expressing conservation of energy: if the induced current aided the change instead of resisting it, the system could amplify itself without external work. In practice, the current direction depends on whether the flux is increasing or decreasing, and on the geometry of the loop and field.
When to use it
Use this law whenever a changing magnetic field, moving magnet, or changing loop area induces a current or emf in a conductor. It is especially useful for solving induction problems involving coils, generators, transformers, braking by eddy currents, and determining current direction with the right-hand rule.
Worked example, step by step
A single circular loop has area A = 0.020 m^2 and its magnetic field perpendicular to the loop increases from 0.50 T to 1.30 T in 0.40 s. Step 1: Compute the change in magnetic flux. \u0394\u03a6_B = A( B_final - B_initial ) \u0394\u03a6_B = 0.020(1.30 - 0.50) \u0394\u03a6_B = 0.020(0.80) = 0.016 Wb Step 2: Find the rate of change of flux. \u0394\u03a6_B / \u0394t = 0.016 / 0.40 = 0.040 Wb/s Step 3: Use Lenz’s law for the induced emf magnitude. |\varepsilon| = N|d\u03a6_B/dt|, with N = 1 |\varepsilon| = 1(0.040) = 0.040 V Step 4: Determine the direction. Because the flux through the loop is increasing in the given field direction, the induced current must produce a magnetic field opposite to that field. Final answer: the induced emf has magnitude 0.040 V, and the current flows in the direction that creates a field opposing the increase in flux.
Common mistakes to avoid
- Forgetting that the minus sign indicates direction, not a negative magnitude of emf
- Using the magnetic field strength alone instead of magnetic flux A\u0394B cos\u03b8
- Saying the induced current always opposes the magnetic field rather than the change in flux
Did You Know?
Lenz's law is nature's pushback — induced currents always oppose the change that created them.
Share this formula
More in Physics Laws & Theorems
View allNewton's First Law (Inertia)
BasicAn object stays at rest or in uniform motion unless acted on by a net force.
Newton's Second Law
BasicNet force equals mass times acceleration (rate of change of momentum).
Newton's Third Law
BasicFor every action there is an equal and opposite reaction.
Conservation of Momentum
IntermediateTotal momentum of an isolated system stays constant.
Conservation of Energy
BasicEnergy cannot be created or destroyed, only transformed.
Archimedes' Principle
IntermediateBuoyant force equals the weight of fluid displaced.