Lenz's Law
Lenz's Law states that the direction of an induced current is always such as to oppose the change in magnetic flux that caused it, thereby acting against the motion or change producing the induction. It is essentially a consequence of the conservation of energy and provides the negative sign in Faraday's Law of Induction. Named after Heinrich Lenz (1804–1865), the law explains why generators require mechanical work to produce electricity and underlies the principle of electromagnetic braking.
Key Formula
EMF = -(dΦ_B / dt) [negative sign encodes Lenz's Law]
LaTeX: \mathcal{E} = -\frac{d\Phi_B}{dt}
| Symbol | Meaning | Unit |
|---|---|---|
| ℰ | Induced EMF (direction given by Lenz's Law) | Volt (V) |
| dΦ_B/dt | Rate of change of magnetic flux | Wb/s |
| − | Negative sign indicating opposition to flux change | Dimensionless |
Worked Example
Problem
A bar magnet is pushed north-pole-first towards a circular conducting loop. Using Lenz's Law, determine the direction of the induced current in the loop as viewed from the magnet's side.
Solution
Step 1: Identify the change in flux. The north pole approaches, so the magnetic flux through the loop is increasing (field lines entering from the magnet's side). Step 2: Apply Lenz's Law. The induced current must oppose the increase in flux, so the induced magnetic field inside the loop must point away from the approaching magnet (i.e., opposing the increase). Step 3: Use the right-hand rule. For the induced field to point away from the magnet (towards the viewer on the magnet's side), the induced current must flow counter-clockwise when viewed from the magnet's side. Step 4: Conclusion. The induced current flows counter-clockwise (as viewed from the magnet), creating a magnetic north pole facing the approaching magnet — repelling it and opposing the motion.
Answer
Induced current flows counter-clockwise (as seen from the magnet's side), opposing the approach of the magnet.
Lenz's Law: Predicting Induced Current Direction for Common Scenarios
| Scenario | Flux Change | Induced Field Direction | Induced Current (from magnet side) | Physical Effect |
|---|---|---|---|---|
| North pole approaching loop | Increasing | Away from magnet | Counter-clockwise | Loop repels magnet |
| North pole withdrawing from loop | Decreasing | Towards magnet | Clockwise | Loop attracts magnet |
| South pole approaching loop | Increasing (opposite) | Towards magnet | Clockwise | Loop repels magnet |
| Coil entering uniform field | Increasing | Opposing external field | Such as to brake motion | Drag force on coil |
| Coil leaving uniform field | Decreasing | Supporting external field | Such as to brake motion | Drag force on coil |
Interactive Tools
PhET Faraday's Law — Lenz's Law Visualization
Observe how current direction opposes flux change in real time
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Faraday's Law of Induction
Faraday's Law of Induction states that the electromotive force (EMF) induced in a closed loop is equal to the negative rate of change of magnetic flux through the loop. This fundamental law explains how changing magnetic fields produce electric currents, forming the basis of electric generators, transformers, and induction motors. It was discovered experimentally by Michael Faraday in 1831 and independently by Joseph Henry around the same time.
Magnetic Flux
Magnetic flux is the total quantity of magnetic field lines passing perpendicularly through a given surface area, measuring how much of the magnetic field is captured by that surface. It is a scalar quantity defined as the dot product of the magnetic field vector and the area vector of the surface. Magnetic flux is fundamental to understanding electromagnetic induction, transformer operation, and the behaviour of inductors in circuits.
Electromagnetic Induction
Electromagnetic induction is the process by which a changing magnetic field within a closed conductor induces an electromotive force (EMF) and consequently an electric current in the conductor. Discovered by Michael Faraday in 1831, it is governed by Faraday's Law and Lenz's Law, and forms the operational basis of virtually all large-scale electrical power generation, transformers, and countless sensing devices. The phenomenon demonstrates the deep relationship between electricity and magnetism, first unified in Maxwell's equations.
Named after Heinrich Friedrich Emil Lenz (1804–1865), a Baltic German physicist who formulated the law in 1834. "Law" derives from Old English "lagu", from Old Norse "log" meaning "something fixed or settled".