Key Idea: Wave a magnet through a coil and a needle flicks, with no battery anywhere: a changing magnetic flux induces an emf (Faraday's law).
Flux
- Φ = BA cos θ
- θ to the normal
- Edge-on: Φ = 0
Faraday and Lenz
- ε = −N ΔΦ/Δt
- Steady flux: no emf
- Current opposes the change
Generators
- Rod: ε = BvL
- Coil: sinusoidal emf
- ω × 2: peak × 2, T ÷ 2
Lenz's law fixes the direction: the induced effect always opposes the change, which is energy conservation. The same idea runs every generator: a coil turning in a field gives a sinusoidal emf, and turning it faster gives taller, more frequent peaks. 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
Not in the booklet: build them from the ones above.
- peak emf (V)
- angular speed of the coil (rad s⁻¹)
- period of the emf (s)
IB-style worked examples
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.
Next:
A coil rotating in a uniform field gives a peak emf of 9.0 V with a period of 60 ms. The coil is turned three times as fast. Determine the new peak emf and period.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Next:
A 400-turn coil of area 0.025 m² faces a 0.080 T field. It turns to edge-on in 4.0 ms. Determine the average emf.
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. A rotating coil's emf is largest when the flux is zero (coil edge-on), and zero when the flux is largest. 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.
A generator's coil turns twice as fast. What happens to its emf? The peak doubles (ε₀ = BANω) and the period halves (T = 2π/ω).
At which coil position is a generator's emf zero? When the coil faces the field: the flux is largest but momentarily not changing.
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.
- Only a CHANGING flux induces an emf — emphasise 'rate of change'.
- A rotating coil: emf zero when it faces the field, largest when it is edge-on (normal at 90° to B).
- For a change of rotation speed, scale the peak by the factor and divide the period by it.