A changing field drives a voltage.

Magnetic flux through a loop is BA $\cos\theta$ , where θ is the angle between the field and the area normal. An emf is induced when the linked flux changes. Lenz’s law sets a direction that opposes the flux change, consistent with energy conservation.

Transformers use changing current to link changing flux between coils. An ideal transformer has voltage ratio equal to turns ratio and equal input and output powers. A steady DC input does not sustain transformer action. Accelerating charges can radiate electromagnetic waves, with oscillating electric and magnetic fields.

INTERACTIVE MODEL

Change flux, induce emf

Number of turns50

READ THE GRAPH

Explore the relationship

Flux through each turn changes by 0.020 Wb. Lenz’s law sets the opposing direction.

Average emf magnitude / V

Tap or focus a plotted point to read its values.

View plotted data as a table

Explore the relationship
Series	Flux-change time / s	Average emf magnitude / V
Average emf magnitude / V	0.1	10
Average emf magnitude / V	0.131667	7.59494
Average emf magnitude / V	0.163333	6.12245
Average emf magnitude / V	0.195	5.12821
Average emf magnitude / V	0.226667	4.41176
Average emf magnitude / V	0.258333	3.87097
Average emf magnitude / V	0.29	3.44828
Average emf magnitude / V	0.321667	3.10881
Average emf magnitude / V	0.353333	2.83019
Average emf magnitude / V	0.385	2.5974
Average emf magnitude / V	0.416667	2.4
Average emf magnitude / V	0.448333	2.23048
Average emf magnitude / V	0.48	2.08333
Average emf magnitude / V	0.511667	1.9544
Average emf magnitude / V	0.543333	1.84049
Average emf magnitude / V	0.575	1.73913
Average emf magnitude / V	0.606667	1.64835
Average emf magnitude / V	0.638333	1.56658
Average emf magnitude / V	0.67	1.49254
Average emf magnitude / V	0.701667	1.42518
Average emf magnitude / V	0.733333	1.36364
Average emf magnitude / V	0.765	1.30719
Average emf magnitude / V	0.796667	1.25523
Average emf magnitude / V	0.828333	1.20724
Average emf magnitude / V	0.86	1.16279
Average emf magnitude / V	0.891667	1.1215
Average emf magnitude / V	0.923333	1.08303
Average emf magnitude / V	0.955	1.04712
Average emf magnitude / V	0.986667	1.01351
Average emf magnitude / V	1.01833	0.981997
Average emf magnitude / V	1.05	0.952381
Average emf magnitude / V	1.08167	0.924499
Average emf magnitude / V	1.11333	0.898204
Average emf magnitude / V	1.145	0.873362
Average emf magnitude / V	1.17667	0.849858
Average emf magnitude / V	1.20833	0.827586
Average emf magnitude / V	1.24	0.806452
Average emf magnitude / V	1.27167	0.78637
Average emf magnitude / V	1.30333	0.767263
Average emf magnitude / V	1.335	0.749064
Average emf magnitude / V	1.36667	0.731707
Average emf magnitude / V	1.39833	0.715137
Average emf magnitude / V	1.43	0.699301
Average emf magnitude / V	1.46167	0.684151
Average emf magnitude / V	1.49333	0.669643
Average emf magnitude / V	1.525	0.655738
Average emf magnitude / V	1.55667	0.642398
Average emf magnitude / V	1.58833	0.629591
Average emf magnitude / V	1.62	0.617284
Average emf magnitude / V	1.65167	0.605449
Average emf magnitude / V	1.68333	0.594059
Average emf magnitude / V	1.715	0.58309
Average emf magnitude / V	1.74667	0.572519
Average emf magnitude / V	1.77833	0.562324
Average emf magnitude / V	1.81	0.552486
Average emf magnitude / V	1.84167	0.542986
Average emf magnitude / V	1.87333	0.533808
Average emf magnitude / V	1.905	0.524934
Average emf magnitude / V	1.93667	0.516351
Average emf magnitude / V	1.96833	0.508044
Average emf magnitude / V	2	0.5

Probe along the horizontal axis0.1Average emf magnitude / V: 10

Explore: Keep the flux change fixed and halve its duration. Compare induced emf.

\Phi=BA\cos\theta\quad\mathcal E=-N\frac{\Delta\Phi}{\Delta t}\quad\frac{V_p}{V_s}=\frac{N_p}{N_s}\quad I_pV_p=I_sV_s

WORKED EXAMPLE

Flux per turn changes by 0.012 Wb in 0.10 s through a 50-turn coil.

Average emf magnitude = N|ΔΦ|/Δt.
50 × $\frac{0.012}{0.10}$ = 6 V.

Assumed knowledge

AC circuits, energy and power.

Learning checkpoints & source

YOUR LEARNING CHECKPOINT

Use flux, Faraday’s law and Lenz’s law.
Explain transformers and electromagnetic radiation.

QCAA Physics · Unit 3 · Electromagnetism ↗

READY TO TRY IT?

A changing field drives a voltage.

Change flux, induce emf

Explore the relationship

Flux per turn changes by 0.012 Wb in 0.10 s through a 50-turn coil.

Put the idea to work.