Physics • Year 12 • Module 6 • Lesson 13
Faraday's Law of Induction
Lock in the core vocabulary, the Faraday's Law formula, and the key insight that it is the rate of change of flux — not the total flux — that drives induction.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: Faraday's Law, induced emf, rate of change of flux, number of turns (N), magnetic flux, Lenz's Law, electromagnetic induction, eddy currents, flux linkage, tesla. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | A voltage produced in a conductor when the magnetic flux through it changes. | |
| 1.2 | The law stating that induced emf equals the negative rate of change of magnetic flux multiplied by the number of turns: ε = −N ΔΦ/Δt. | |
| 1.3 | The quantity ΔΦ/Δt, measured in Wb/s = V, that determines the magnitude of the induced emf. | |
| 1.4 | The phenomenon by which a changing magnetic field produces an electric current in a nearby conductor. | |
| 1.5 | The total magnetic flux passing through all N turns of a coil: NΦ. | |
| 1.6 | Loops of current induced in bulk conducting materials by changing magnetic flux, causing energy dissipation. | |
| 1.7 | The law stating that the direction of an induced current is such that it opposes the change in flux that produced it. | |
| 1.8 | The number of wire loops in a coil; increasing it multiplies the induced emf for the same flux change. | |
| 1.9 | The product B•A•cosθ, representing the amount of magnetic field passing through a given area. SI unit: weber (Wb). | |
| 1.10 | The SI unit of magnetic field strength, equal to 1 kg/(A•s²). |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 A large, constant magnetic flux of 2.0 Wb through a 500-turn coil will produce a large induced emf. T / F
2.2 Doubling the number of turns in a coil while keeping ΔΦ/Δt constant will double the magnitude of the induced emf. T / F
2.3 The negative sign in Faraday's Law (ε = −NΔΦ/Δt) tells us that induced emf depends on the area of the coil. T / F
2.4 A slower change in magnetic flux will produce a smaller induced emf than a faster change over the same ΔΦ. T / F
2.5 Faraday's Law applies only to coils with multiple turns; single loops have no induced emf. T / F
2.6 Induction cooktops work by inducing eddy currents in the metal pot, which generate heat via the pot's resistance. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)
Word bank:
changing · constant · eddy currents · emf · flux linkage · number of turns · opposes · rate
Faraday's Law states that the induced ___________ in a coil is proportional to the ___________ of change of magnetic flux. For a coil with N turns, this becomes ε = −NΔΦ/Δt, where NΔΦ is called the change in ___________. The negative sign reflects Lenz's Law: the induced emf always ___________ the change in flux that produced it. A key insight is that a ___________ flux produces zero emf, no matter how large it is. Only a ___________ flux induces an emf. Increasing the ___________ amplifies the induced emf proportionally, which is why transformers use many turns. In conducting materials, changing flux induces circulating loops of current called ___________, which are exploited in induction braking and induction cooktops.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 State Faraday's Law in words and write the mathematical formula for a coil of N turns.
4.2 Why does a generator produce a larger emf when it spins faster?
4.3 Explain why a magnet held stationary inside a coil produces no current in the coil.
4.4 Name two real-world applications of Faraday's Law and explain which aspect of the law each exploits.
5. Formula identification
The Faraday's Law formula is shown below. Label each symbol by writing its meaning and SI unit in the table. 8 marks (1 per row)
| Symbol | Meaning (what it represents) | SI unit |
|---|---|---|
| ε | ||
| N | ||
| ΔΦ | ||
| Δt | ||
| − (negative sign) | n/a |
5.2 Circle the quantity in the formula that, if increased while all others remain constant, would have the greatest direct effect on increasing |ε|. Justify your answer in one sentence.
Stuck? Revisit the Faraday's Law formula panel and variable definitions in the lesson.Q1 — Term–definition match
1.1 induced emf • 1.2 Faraday's Law • 1.3 rate of change of flux • 1.4 electromagnetic induction • 1.5 flux linkage • 1.6 eddy currents • 1.7 Lenz's Law • 1.8 number of turns (N) • 1.9 magnetic flux • 1.10 tesla.
Q2 — True / false with correction
2.1 False. A constant flux of any magnitude produces zero induced emf. Faraday's Law requires a changing flux (ΔΦ/Δt ≠ 0) to induce an emf.
2.2 True. |ε| = N · |ΔΦ/Δt|, so doubling N doubles the emf magnitude for the same rate of flux change.
2.3 False. The negative sign in Faraday's Law is a statement of Lenz's Law: the induced emf acts in a direction that opposes the change in flux that produced it. It indicates direction, not dependence on area.
2.4 True. A smaller Δt for the same ΔΦ means a larger ΔΦ/Δt, hence a larger emf. Slower change means smaller ΔΦ/Δt and smaller emf.
2.5 False. Faraday's Law applies to single loops (N = 1) as well. ε = −ΔΦ/Δt for a single loop. Multiple turns amplify the effect because each turn adds its own induced emf in series.
2.6 True. An alternating current in the induction cooktop coil creates a rapidly changing magnetic field, which induces eddy currents in the metal pot's base; these eddy currents heat the pot via resistive (Joule) heating.
Q3 — Cloze paragraph
In order: emf / rate / flux linkage / opposes / constant / changing / number of turns / eddy currents.
Q4.1 — State Faraday's Law
Faraday's Law states that the magnitude of the induced emf in a coil is equal to the number of turns multiplied by the rate of change of magnetic flux through the coil. Mathematically: ε = −NΔΦ/Δt, where ε is in volts, N is dimensionless, ΔΦ is in webers, and Δt is in seconds.
Q4.2 — Why faster spinning gives larger emf in a generator
A faster-spinning generator increases the rate at which the coil cuts through magnetic field lines, so the flux through the coil changes more quickly (ΔΦ/Δt is larger). By Faraday's Law (ε = −NΔΦ/Δt), a larger rate of flux change produces a larger induced emf.
Q4.3 — Stationary magnet inside coil produces no current
A stationary magnet creates a constant magnetic flux through the coil. Because ΔΦ = 0 (flux is not changing), Faraday's Law gives ε = −N × 0/Δt = 0 V. With zero induced emf there is no current. Induction requires a changing flux, not merely the presence of a flux.
Q4.4 — Two real-world applications
Accept any two of: (1) Generators — exploit the continuous change in flux as a coil rotates in a field; each rotation cycle sweeps out a changing flux, inducing an alternating emf. (2) Transformers — exploit the N-multiplication: a large N on the secondary coil amplifies the induced emf relative to the primary, or vice versa. (3) Induction cooktops — exploit eddy currents driven by a rapidly changing flux in the pot base. (4) Wireless charging — a transmitter coil creates a changing field that induces emf in a receiver coil via Faraday's Law.
Q5 — Formula identification
ε: induced electromotive force (emf); unit = volt (V). N: number of turns in the coil; dimensionless (no unit). ΔΦ: change in magnetic flux; unit = weber (Wb). Δt: time interval; unit = second (s). − sign: indicates Lenz's Law — direction of induced emf opposes the change in flux; no unit.
5.2 Any of N, ΔΦ, or Δt can be argued. The best answer: decreasing Δt (making the flux change occur faster) increases |ε| because emf is inversely proportional to Δt — halving the time doubles the emf. Increasing N or ΔΦ also increases |ε| proportionally. Accept any valid, justified response. Award 1 mark for circling a symbol and 1 mark for a correct one-sentence justification referencing Faraday's Law.