This physics grades 11-12 lesson on electromagnetic induction notes gives the key ideas first, then worked examples and diagrams. After that, practise with the worksheet on electromagnetic induction and check yourself with the quiz.
Quick answer: Electromagnetic induction is the creation of an emf in a circuit when the magnetic flux linked with it changes. The size is ε = N ΔΦ/Δt (Faraday’s law), where flux Φ = BA cos θ, and the induced current opposes the change (Lenz’s law). Generators use a rotating coil to produce alternating emf.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB D.4
Electromagnetic induction notes: the key ideas
What is magnetic flux?
Hold a hoop in a stream of water and the amount flowing through depends on the hoop’s size and tilt. Magnetic flux works the same way for field lines. It counts how much magnetic field passes through a surface, and it is the quantity whose change creates an emf.
Magnetic flux Φ through a flat surface of area A in a uniform field B is Φ = BA cos θ, where θ is the angle between the field and the normal to the surface. The unit is the weber (Wb): 1 Wb = 1 T m².
What do Faraday’s and Lenz’s laws say?
An emf appears in a circuit whenever the flux linked with it changes, whether the field changes, the area changes or the angle changes. Michael Faraday found that the size depends on how fast the change happens, and Heinrich Lenz found the direction.
Faraday: ε = −N ΔΦ/Δt. The induced emf equals the rate of change of flux linkage NΦ.
Lenz: the minus sign shows that the induced current opposes the change that causes it.
A coil of 200 turns and area 25 cm² faces a field that rises from 0 to 0.40 T in 0.050 s. Calculate the average emf.
A = 25 × 10⁻⁴ = 2.5 × 10⁻³ m². ΔΦ = BA = 0.40 × 2.5 × 10⁻³ = 1.0 × 10⁻³ Wb. ε = NΔΦ/Δt = 200 × 1.0 × 10⁻³ / 0.050 = 4.0 V.
How is an emf made by a moving conductor?
A rod of length L moving at speed v across a field sweeps out area at the rate Lv, so the flux through the circuit changes at the rate BLv. The emf is therefore ε = BLv, and if the rod is part of a closed circuit a current flows.
ε = B L v (rod perpendicular to B and to its motion)
ε = emf (V), B = flux density (T), L = length of rod in the field (m), v = speed (m/s).
A rod 0.60 m long slides at 5.0 m/s across a 0.25 T field in a circuit of total resistance 1.5 Ω. Calculate the current and the force needed to keep it moving.
ε = BLv = 0.25 × 0.60 × 5.0 = 0.75 V. I = ε/R = 0.75 / 1.5 = 0.50 A. The magnetic force opposing the motion is F = BIL = 0.25 × 0.50 × 0.60 = 0.075 N, so the pushing force must be 0.075 N. Check: Fv = 0.375 W = I²R.
How does a generator work?
A coil turning in a field has a flux that varies with the angle, so an emf is induced all the time. The result is a sinusoidal alternating emf whose peak value depends on the number of turns, the field, the area and the angular speed.
How do the factors compare?
| Change made | Effect on peak emf of a generator | Effect on frequency |
|---|---|---|
| Double the turns N | doubles | unchanged |
| Double the field B | doubles | unchanged |
| Double the rotation rate | doubles | doubles |
| Replace coil with one of half the area | halves | unchanged |
Students think a large flux gives a large emf. It is the rate of change of flux that matters: a strong steady field linked with a stationary coil induces nothing.
Ask “what is changing?” first: B, A or θ. Then ask “which way would the induced field have to point to resist it?” That second step is Lenz’s law and it gives the current direction.
- Flux: Φ = BA cos θ, measured in weber (1 Wb = 1 T m²).
- Faraday’s law: ε = −N ΔΦ/Δt.
- Lenz’s law: the induced current opposes the change that causes it.
- Moving rod: ε = BLv.
- Generator: ε = NBAω sin ωt, peak ε₀ = NBAω.
How changing flux creates an emf: frequently asked questions
What is the difference between flux and flux density?
Flux density B is the field strength in tesla. Flux Φ = BA cos θ is the amount of field passing through a surface and is measured in weber.
Why is there a minus sign in Faraday’s law?
The minus sign expresses Lenz’s law. The induced emf drives a current whose magnetic effect opposes the change of flux, which is also a consequence of energy conservation.
Can a steady magnetic field induce a current?
Not by itself. An emf is induced only while the flux through the circuit is changing, for example when the coil moves, rotates or the field varies.
How can a generator’s emf be increased?
Use more turns, a stronger magnet, a larger coil area or a faster rotation. Each of these increases the peak value ε₀ = NBAω.
How does Lenz’s law relate to conservation of energy?
If the induced current helped the change, energy would appear from nothing. Because it opposes the change, work must be done to move the magnet or rod, and that work becomes electrical energy.
