Lenz's law tells us the direction of an induced current when magnetic flux through a circuit changes. It matters because changing magnetic fields are the basis of generators, transformers, induction cooktops, metal detectors, and many sensors. The key idea is that nature resists the change in magnetic flux, not the magnetic field itself.
In a coil, this resistance appears as an induced current that creates its own magnetic field.
Key Facts
- Lenz's law: The induced current flows in the direction that creates a magnetic field opposing the change in magnetic flux.
- Faraday's law with Lenz's law: ε = -N ΔΦB/Δt, where the minus sign shows opposition to the change.
- Magnetic flux: ΦB = B A cos θ, where θ is the angle between the magnetic field and the area vector.
- If a north pole moves toward a coil, the near face of the coil becomes a north pole to repel the approaching magnet.
- If the magnetic flux through a coil is not changing, the induced emf is zero: ΔΦB/Δt = 0.
- Eddy-current braking uses induced currents in a conductor to create magnetic forces that oppose motion and convert kinetic energy into thermal energy.
Vocabulary
- Lenz's law
- Lenz's law states that an induced current creates a magnetic field that opposes the change in magnetic flux that produced it.
- Magnetic flux
- Magnetic flux is a measure of how much magnetic field passes through a surface.
- Induced emf
- Induced emf is the voltage produced in a circuit by a changing magnetic flux.
- Induced current
- Induced current is the electric current that flows when an induced emf acts in a closed conducting path.
- Eddy current
- An eddy current is a looping current induced inside a solid conductor by a changing magnetic field.
Common Mistakes to Avoid
- Saying the induced current opposes the magnetic field itself is wrong because it opposes the change in magnetic flux, which depends on field strength, area, and angle.
- Ignoring the negative sign in ε = -N ΔΦB/Δt is wrong because the sign represents the direction predicted by Lenz's law.
- Assuming a current is induced whenever a magnet is nearby is wrong because a steady magnet and a stationary coil produce no changing flux and no induced emf.
- Using the right-hand rule without first deciding whether flux is increasing or decreasing is wrong because the current direction depends on the change that must be opposed.
Practice Questions
- 1 A 50-turn coil has its magnetic flux per turn increase from 0.020 Wb to 0.080 Wb in 0.30 s. What is the magnitude of the induced emf?
- 2 A coil of area 0.040 m2 is perpendicular to a magnetic field that increases uniformly from 0.10 T to 0.60 T in 0.25 s. If the coil has 200 turns, what is the magnitude of the induced emf?
- 3 A north pole of a bar magnet moves toward the left face of a circular coil. Explain which magnetic pole the left face of the coil becomes and why this agrees with conservation of energy.