Lenz Law
Induced currents oppose the change producing them.
Formula
Variables
Example
Explains the minus sign in Faraday law
How it works
When the magnetic flux through a loop changes, a current is induced in a direction that creates its own magnetic field to resist that change. This is nature’s built-in "pushback" against sudden increases or decreases in flux, and it is a direct consequence of energy conservation: the induced current cannot help the change without an external source doing work. The rule tells you the direction of the induced current, not its size.
When to use it
Use this law whenever a changing magnetic field, moving magnet, or moving conductor produces an induced current. It is especially useful for deciding current direction in generators, inductors, eddy currents, and electromagnetic braking problems.
Worked example, step by step
A circular coil has 80 turns and area 0.020 m^2. The magnetic field through the coil increases from 0.30 T to 0.50 T in 0.10 s, and the coil resistance is 4.0 Ω. Step 1: Find the change in magnetic flux per turn: ΔΦ = AΔB = 0.020 × (0.50 - 0.30) = 0.0040 Wb Step 2: Find the induced emf magnitude: ε = N(ΔΦ/Δt) = 80 × (0.0040 / 0.10) = 3.2 V Step 3: Find the induced current: I = ε/R = 3.2 / 4.0 = 0.80 A Step 4: Direction: because the magnetic field through the coil is increasing, the induced current flows so that its magnetic field opposes that increase. Final answer: I = 0.80 A, and its direction is such that it creates a field opposing the rising magnetic field.
Common mistakes to avoid
- Thinking the induced current opposes the magnetic field itself rather than the change in flux
- Forgetting that a decrease in flux also produces an opposing response, but in the opposite current direction
- Using Lenz's law to calculate the current magnitude instead of only the direction or sign
Did You Know?
Lenz's law is nature enforcing energy conservation: induced currents always oppose the change that made them.
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