5dFaraday's Law and Lenz's Law
Apply Faraday's law and Lenz's law to determine induced EMF and current direction, and explore eddy currents, self-inductance, and back-EMF in motors.
Faraday's and Lenz's laws explain the direction and magnitude of every induced current — from the generator at a power plant to the wireless charger on your desk. Understanding them completes the picture of electromagnetism.
Lesson Overview
Faraday's law and Lenz's law together describe how and in what direction an EMF is induced by a changing magnetic flux. In this lesson you will apply Faraday's law (EMF = −dΦ/dt), use Lenz's law to determine the direction of induced current, understand eddy currents and self-inductance, and explore how AC generation and back-EMF in motors arise from these principles.
Key Concepts
Faraday's Law
EMF = −dΦ/dt (or −NΔΦ/Δt); the rate of flux change determines the magnitude of induced EMF
Lenz's Law
The induced current flows in a direction that opposes the change in flux that caused it (conservation of energy)
Eddy Currents
Circulating currents induced in bulk conductors by changing B; cause heating and braking forces
Self-Inductance (L)
A coil opposes changes in its own current; EMF = −L(dI/dt); unit: henry (H)
Mutual Inductance
Changing current in one coil induces EMF in a nearby coil; basis of transformers
Back-EMF in Motors
A spinning motor coil generates an opposing EMF that limits current and represents energy conversion
A coil of 60 turns has a flux that changes at a rate of 0.030 Wb/s. Calculate the induced EMF.
A bar magnet's north pole is pushed toward a horizontal coil. Using Lenz's law, determine the direction of the induced current as viewed from above.
An inductor has L = 0.50 H. The current through it changes from 2.0 A to 6.0 A in 0.10 s. Find the self-induced EMF.
A DC motor runs at full speed with a back-EMF of 100 V on a 120 V supply. The coil resistance is 2.0 Ω. Calculate the current through the motor at full speed.
Explain why eddy currents are useful in magnetic braking systems (e.g., roller coasters, train brakes).
A 100-turn coil has flux changing from 0.040 Wb to 0.010 Wb in 0.050 s. Find the induced EMF.
Hint: Use EMF = −N(ΔΦ/Δt). Calculate ΔΦ = final − initial first.
A magnet is pulled away from a coil. Using Lenz's law, does the induced current attract or repel the magnet?
Hint: If flux is decreasing, the induced current must try to maintain it. What pole does the coil present to the retreating magnet?
An inductor of L = 0.20 H carries a current that decreases at 5.0 A/s. What is the self-induced EMF and in which direction does it act?
Hint: Use EMF = −L(dI/dt). A decreasing current means dI/dt is negative. The inductor opposes the decrease.
Why does a motor draw more current when it first starts than when running at full speed?
Hint: Consider the back-EMF: at startup, the coil is not yet spinning, so back-EMF = 0. What limits the current then?
A transformer primary has 500 turns and the secondary has 50 turns. If the primary current changes at 2.0 A/s and the mutual inductance M = 0.10 H, find the induced EMF in the secondary.
Hint: For mutual inductance: EMF_s = −M(dI_p/dt).
Key Vocabulary
Lenz's Law
The induced current in a conductor always flows in a direction that opposes the change in magnetic flux that produced it, consistent with conservation of energy.
Example: When a magnet approaches a coil, the induced current creates a magnetic field that repels the magnet, opposing its motion.
Eddy Currents
Loops of electric current induced within a bulk conductor when it is exposed to a changing magnetic field; they dissipate energy as heat.
Example: Eddy currents in the metal disc of an induction cooktop generate heat to cook food.
Self-Inductance (L)
The property of a coil by which a change in current induces an opposing EMF in the same coil; EMF = −L(dI/dt); measured in henries (H).
Example: A large inductor in a circuit resists sudden changes in current, smoothing out fluctuations.
Back-EMF
The EMF generated by a spinning motor coil that opposes the supply voltage, limiting current and representing the conversion of electrical energy to mechanical energy.
Example: A motor stalled (not spinning) has no back-EMF and draws dangerously high current.
Interactive Practice — 5 Questions
Lenz's law states that the induced current:
The SI unit of self-inductance is the:
An inductor (L = 0.40 H) has current changing at 3.0 A/s. What is the self-induced EMF?
Eddy currents in a conductor moving through a magnetic field cause:
Back-EMF in a motor is largest when the motor is:
Independent Practice
A 200-turn coil experiences a flux change from 0.080 Wb to 0.020 Wb in 0.040 s. Calculate the induced EMF and state the significance of the negative sign.
A north pole of a magnet is moved away from a coil. Using Lenz's law, determine the direction of the induced current and explain whether the coil attracts or repels the magnet.
An inductor (L = 0.60 H) in a circuit has its current reduced from 4.0 A to 1.0 A in 0.15 s. Calculate the self-induced EMF and explain how it affects the circuit.
A motor operates on 240 V and has a coil resistance of 3.0 Ω. At full speed, the current is 4.0 A. Calculate the back-EMF at full speed.
★ Explain how eddy currents are both useful (induction cooktops, magnetic braking) and harmful (energy loss in transformer cores). How do engineers minimize harmful eddy currents in transformer cores?
ChallengeCommon Mistakes
Thinking Lenz's law means the induced current cancels the flux entirely.
The induced current opposes the change in flux, not the flux itself. It cannot fully cancel the change — that would violate energy conservation.
Confusing self-inductance EMF = −L(dI/dt) with Faraday's law EMF = −N(dΦ/dt).
Both express the same physics. For a coil, L = NΦ/I, so they are equivalent. Use −L(dI/dt) when L is given; use −N(dΦ/dt) when flux data is given.
Assuming a motor draws the same current at startup and full speed.
At startup, back-EMF = 0 and current = V/R (very high). At full speed, back-EMF reduces the net voltage and current drops significantly.
Math Tips
For Lenz's law direction: (1) Determine if flux is increasing or decreasing. (2) The induced current creates a field to oppose that change. (3) Use the right-hand rule to find the current direction from the induced field direction.
Back-EMF formula: V_supply = back-EMF + I·R. Rearrange to find any unknown: back-EMF = V_supply − IR.