PHYC10004 Chap.8 Electromagnetic Induction: Faraday and Lenz
Electromagnetic Induction: Faraday and Lenz
Electromagnetic induction is how almost all electrical power is generated. Faraday's law states that a changing magnetic flux through a circuit induces an emf equal to minus the rate of change of that flux, ε = −N dΦ/dt for a coil of N turns.
The flux can change because the field changes, because the area changes, or because the coil rotates, which is how an AC generator produces a sinusoidal emf.
Lenz's law, the minus sign in Faraday's law, fixes the direction: the induced current opposes the change that caused it, a consequence of energy conservation.
This chapter turns Lenz's law into a three-question routine and applies it to magnets and coils, jumping rings, eddy-current damping and magnets falling through pipes. It derives the motional emf BLv of a sliding rod, introduces the induced electric field and the displacement current that completes Ampere's law, and collects the four Maxwell equations.
Past papers pair one emf calculation with a written explanation of an induction phenomenon.
What this chapter covers
- 01
Magnetic Flux
- 02
Faraday's Law
- 03
Lenz's Law
- 04
Motional Emf
- 05
The AC Generator
- 06
Eddy Currents
- 07
Induced Electric Fields
- 08
Displacement Current
- 09
Maxwell's Equations
Worked example · free
Peak emf of a rotating generator coil
- 1Flux through the coil: Φ = NBA cos ωt, with ω = 2π × 60 = 377 rad/s.
- 1Faraday: ε = −dΦ/dt = NBAω sin ωt, so the peak is NBAω.
- 1Peak emf: 200 × 0.40 × 5.0 × 10⁻³ × 377 = 151 V.
- 1Doubling the rotation rate doubles ω and so doubles the peak emf to about 302 V, and also halves the period.
Key terms
- Magnetic Flux
- Magnetic flux is the integral of B · dA over a surface, equal to BA cos θ for a uniform field, measured in webers.
- Faraday's Law
- Faraday's law states that the emf induced around a circuit equals minus the rate of change of magnetic flux through it, multiplied by the number of turns.
- Lenz's Law
- Lenz's law states that an induced current flows in the direction whose magnetic field opposes the change in flux that produced it.
- Motional Emf
- Motional emf is the emf BLv produced across a conductor of length L moving at speed v perpendicular to a magnetic field B.
- Eddy Current
- An eddy current is a loop of induced current within a bulk conductor exposed to a changing flux, which dissipates energy and opposes the motion causing it.
- Displacement Current
- Displacement current is the term ε₀ dΦ_E/dt that Maxwell added to Ampere's law so that a changing electric field also produces a magnetic field.
Electromagnetic Induction: Faraday and Lenz FAQ
How do I find the direction of an induced current?
Ask three questions: which way does the external field point through the loop, is its flux increasing or decreasing, and which induced field would oppose that change? Then use the right-hand grip rule to turn the induced field direction into a current direction.
Why is Lenz's law a statement of energy conservation?
If the induced current reinforced the change that produced it, a tiny push on a magnet would generate a current that pulled the magnet faster, producing ever more current with no energy input. Opposing the change means work must be done, and that work becomes electrical energy.
Why does a ring with a cut in it not jump off a coil?
The changing flux still induces an emf around the cut ring, but with no closed path no current can flow. Without an induced current there is no opposing magnetic field and therefore no repulsive force to throw the ring upward.
What is the displacement current and why is it needed?
Between the plates of a charging capacitor no charge flows, yet a magnetic field is measured there. Maxwell's displacement current, ε₀ times the rate of change of electric flux, accounts for it and makes Ampere's law consistent for changing fields.
Exam move
Drill Lenz's law until it is mechanical, using magnets approaching and leaving loops, currents switched on and off near a coil, and rings on solenoids, writing the three questions each time. Pair each direction answer with a number: an average emf from a flux change, including the doubling when a field reverses, a generator's peak emf, and a sliding rod's emf, current and force.
Then write half-page explanations of a jumping ring, eddy-current damping and the displacement current, each naming the relevant Maxwell equation.
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