Key Idea: Wave a magnet through a coil and a needle flicks — no battery anywhere. That single idea — a changing magnetic flux induces a voltage (emf), Faraday's law — runs every generator and transformer on the grid. Lenz's law fixes the direction (the induced effect always opposes the change, conserving energy). It is HL only (D.4).
📐 The formulas you're given
- magnetic flux (Wb); θ is between B and the NORMAL to the area
- induced emf (V); the minus sign is Lenz's law
- motional emf of a rod length L moving at v through field B
- peak emf ε₀ of a coil (N turns, area A) rotating at ω
- rms current — the equivalent DC for the same heating
- transformer turns ratio (ideal: power is conserved)
✏️ IB-style worked examples (one per micro)
The magnetic flux through a 50-turn coil falls steadily from 0.20 Wb to 0 in 0.10 s. Determine the magnitude of the induced emf.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A step-down transformer has 1000 primary turns and 50 secondary turns, with 230 V across the primary. Determine the secondary voltage.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A mains supply has a peak voltage of 325 V. Determine its rms voltage.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Important: 1. Flux uses cos θ to the normal of the area — when B is along the plane of the coil, the flux is zero, not maximum. 2. The minus sign in Faraday's law is Lenz's law (opposition = energy conservation), not an arithmetic error. 3. Don't confuse rms and peak — divide the peak by √2. 4. It is the rate of change of flux that matters — a large but steady flux induces no emf.
Tap each card to reveal the answer.
What does magnetic flux depend on? Φ = BA cos θ — the field B, the area A, and the angle θ between B and the normal to the area.
State Faraday's law. The induced emf equals the rate of change of flux linkage: ε = −N ΔΦ/Δt.
State Lenz's law. The induced current opposes the change that caused it — a consequence of energy conservation (the minus sign).
Motional emf of a 0.40 m rod at 3.0 m/s in a 0.50 T field? 0.60 V — ε = BvL = 0.50 × 3.0 × 0.40.
Why are rms values used for AC? They give the equivalent DC that delivers the same average power (heating).
What does an ideal transformer conserve? Power — so stepping voltage up steps current down (and vice versa).
Exam tips
- Always measure the flux angle to the NORMAL of the area, not to the surface.
- Quote the minus sign as Lenz's law; it is direction, not a negative emf.
- Divide a peak value by √2 to get rms (and ×√2 to go back).
- Only a CHANGING flux induces an emf — emphasise 'rate of change'.
- For transformers, use the turns ratio and remember power is conserved (ideal).