The shape of the lesson
By the end of the lesson, learners can
- Faster change, bigger e.m.f: As the magnet moves through the coil the flux linkage rises and falls, and the e.m.f. follows its rate of change, reversing as the magnet leaves instead of enters.
- Spin a coil: flux linkage: Instead of a magnet moving in a straight line, spin a coil of N turns in the field.
- Flux, linkage, and two laws: Build the definitions up to Faraday and Lenz.
- On a conductor: F = BIL sinθ; the tesla is defined from B = F/(IL) (N A⁻¹ m⁻¹).
- On a charge: F = BQv sinθ, always perpendicular to v, so the path is a circle with r = mv/BQ.
- Induction: Φ = BA, flux linkage = NΦ, induced e.m.f. = rate of change of flux linkage (Faraday); direction opposes the change (Lenz).
One picture every idea returns to
The magnetic flux through a coil is Φ = BA, and for N turns the flux linkage is NΦ. Faraday's law: the induced e.m.f. equals the rate of change of flux linkage. Lenz's law: the induced current flows so as to oppose the change producing it, which is energy conservation in action.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, A changing field makes a voltage.. Move a magnet near a coil and a voltage appears from nowhere. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Faster change, bigger e.m.f | As the magnet moves through the coil the flux linkage rises and falls, and the e.m.f. follows its rate of change, reversing as the magnet leaves instead of enters. Project tab 5 of the lab (Electromagnetic induction) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Spin a coil: flux linkage | Instead of a magnet moving in a straight line, spin a coil of N turns in the field. Project the simulation and let a student drive it while the class predicts. | Pairs |
| 21 to 30 min | Teach and check: Flux, linkage, and two laws | Build the definitions up to Faraday and Lenz. | Think-Pair-Share |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (4 questions, 47 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Flux, linkage, and two laws, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Think-Pair-Share
Pose the question, give thirty seconds of silent thinking, then a minute to compare with a partner before a few pairs share with the class. The silent minute is the part that cannot be cut.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| The e.m.f. depends on the rate of change of flux linkage, not on the flux itself: a strong magnet held still inside a coil induces no e.m.f. | Always include the number of turns N (use flux linkage NΦ). Lenz's law fixes the direction, and follows from conservation of energy. For an area not perpendicular to the field, use the perpendicular component (Φ = BA cosθ). |
Electromagnetic induction: topic worksheet
4 questions, 47 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
A flat coil of 200 turns, each of area 1.5 × 10⁻³ m², lies with its plane perpendicular to a magnetic field. The flux density increases steadily from 0 to 0.40 T in a time of 0.20 s.
(a) Define magnetic flux. [1]
(b) Calculate the change in magnetic flux linkage. [3]
(c) Calculate the e.m.f. induced in the coil. [2]
(d) State Faraday's law of electromagnetic induction. [2]
(e) State Lenz's law, and the conservation principle it expresses. [2]
(f) State the effect on the induced e.m.f. of doubling the number of turns. [1]
Fig. 8.1 shows how the magnetic flux linkage through a search coil varies with time as a magnet is moved near it.
(a) State how the induced e.m.f. is obtained from this graph. [1]
(b) Calculate the induced e.m.f. during the first 0.30 s. [3]
(c) State the induced e.m.f. between 0.30 s and 0.70 s, and explain your answer. [2]
(d) Compare the size and sign of the e.m.f. after 0.70 s with that in the first 0.30 s. [2]
(e) State the general effect on the induced e.m.f. of moving the magnet more quickly. [2]
A metal rod of length 0.25 m rests on two horizontal rails and is pulled along them at a steady 4.0 m s⁻¹. A uniform magnetic field of flux density 0.30 T is perpendicular to the plane of the rails, as in Fig. 9.1. The rails are joined by a resistor of resistance 0.50 Ω.
(a) Show that the e.m.f. induced across the rod is given by ε = BLv, and calculate its value. [3]
(b) Calculate the current driven through the resistor. [2]
(c) The current in the rod lies in the magnetic field. Calculate the force on the rod due to this current. [2]
(d) State the direction of this force relative to the motion, and name the law that gives it. [2]
(e) Explain, using energy, why a force must be applied to keep the rod moving at constant speed. [2]
(f) State and explain the effect on this opposing force of doubling the speed. [2]
This question links three lessons of the topic. A long solenoid carries a current and a coil of 500 turns is wound around its middle.
(a) Describe the magnetic field inside the solenoid, and state the effect of placing a soft iron core inside it. [2]
(b) The current is switched off, and the flux linkage of the 500-turn coil falls from 0.080 Wb to zero in 0.040 s. Calculate the average e.m.f. induced. [3]
(c) State the direction of the induced current relative to the change, and the law used. [2]
(d) An electron now enters the solenoid's field of flux density 0.015 T at 2.0 × 10⁶ m s⁻¹, at right angles to the field. Calculate the radius of its circular path. [3]
(e) State and explain the effect on this radius of doubling the flux density. [2]
(f) State why the magnetic force on the electron does not change its speed. [1]
Answer key and marking notes
- (a)Magnetic flux Φ = BA, the product of flux density and the perpendicular area ✓
- (b)ΔΦ = BA = 0.40 × 1.5 × 10⁻³ = 6.0 × 10⁻⁴ Wb ✓; Δ(NΦ) = 200 × 6.0 × 10⁻⁴ ✓ = 0.12 Wb (weber-turns) ✓
- (c)ε = Δ(NΦ)/Δt = 0.12 / 0.20 ✓ = 0.60 V ✓
- (d)The induced e.m.f. is proportional to the rate of change of magnetic flux linkage ✓✓
- (e)The induced current is in a direction so as to oppose the change producing it ✓; this is conservation of energy ✓
- (f)It doubles ✓
- (a)It is the gradient (rate of change) of the flux-linkage against time graph ✓
- (b)ε = Δ(NΦ)/Δt = (0.50 − 0.20)/0.30 ✓✓ = 1.0 V ✓
- (c)Zero ✓; the flux linkage is constant, so there is no rate of change and no e.m.f. ✓
- (d)Same size (1.0 V from the equal but opposite gradient over 0.40 s gives 0.75 V) but opposite sign: the gradient is −(0.30)/0.40 = −0.75 V ✓, so it is 0.75 V in the opposite direction ✓
- (e)The e.m.f. is larger ✓, because the flux linkage changes at a greater rate ✓
- (a)In a time Δt the rod sweeps area ΔA = L v Δt, so ΔΦ = B L v Δt ✓; ε = ΔΦ/Δt = BLv ✓. ε = 0.30 × 0.25 × 4.0 = 0.30 V ✓
- (b)I = ε/R = 0.30 / 0.50 ✓ = 0.60 A ✓
- (c)F = BIL = 0.30 × 0.60 × 0.25 ✓ = 0.045 N ✓
- (d)It opposes the motion (acts backwards) ✓; this follows from Lenz's law ✓
- (e)Work done against this opposing force ✓ is transferred to electrical energy and then heat in the resistor; with no applied force the rod would slow down ✓
- (f)It doubles ✓; the e.m.f. and current both double, and F = BIL is proportional to the current, hence to the speed ✓
- (a)Strong and almost uniform inside (parallel, equally spaced lines) ✓; a soft iron core greatly increases the flux density ✓
- (b)ε = Δ(NΦ)/Δt. Here the quoted flux linkage falls from 0.080 to 0 Wb ✓; ε = 0.080 / 0.040 ✓ = 2.0 V ✓
- (c)The induced current acts to oppose the fall in flux (it tries to maintain it) ✓; this is Lenz's law ✓
- (d)r = mv/BQ = (9.11 × 10⁻³¹ × 2.0 × 10⁶)/(0.015 × 1.6 × 10⁻¹⁹) ✓✓ = 7.6 × 10⁻⁴ m (0.76 mm) ✓
- (e)The radius halves ✓, since r = mv/BQ is inversely proportional to B ✓
- (f)The force is always perpendicular to the velocity, so it does no work ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
The magnetic flux through a flat coil of area A in a field of flux density B perpendicular to it is:
- AΦ = BA
- BΦ = B / A
- CΦ = A / B
- DΦ = BA²
Faraday's law states that the magnitude of the induced e.m.f. is proportional to the rate of change of:
- Amagnetic flux linkage
- Bmagnetic flux density
- Cthe current in the coil
- Dthe coil's resistance
Lenz's law, that the induced current opposes the change producing it, is a direct consequence of the conservation of:
- Aenergy
- Bcharge
- Cmomentum
- Dmagnetic flux
A bar magnet is held stationary inside a coil. The e.m.f. induced in the coil is:
- Azero
- Ba maximum
- Cequal to BA
- Dproportional to the flux
Quiz key
Flux is flux density times the perpendicular area, Φ = BA, measured in weber (1 Wb = 1 T m²).
The induced e.m.f. equals the rate of change of flux linkage, ε = N ΔΦ/Δt.
If the induced current helped the change, energy would be created from nothing. Opposing it means you must do work, which becomes the electrical energy.
With the magnet still the flux linkage is not changing, so its rate of change is zero and no e.m.f. is induced, however strong the magnet.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.