Year 12 Physics Module 6: Electromagnetism IQ3: Fields Related Lessons 13–19 45 min

Checkpoint 3: Electromagnetic Induction

Test your understanding of AC generators, magnetic flux, Faraday's Law, Lenz's Law, and transformers. Covers displayed Lessons 13–19.

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Lesson 11

AC Generators

  • Flux: $\Phi = BA \cos(\omega t)$
  • Induced emf: $\varepsilon = NBA\omega \sin(\omega t)$
  • Slip rings maintain contact without reversing current
Lesson 12

Magnetic Flux and Changing Flux

  • Flux depends on B, A, and orientation
  • Only changing flux induces emf
  • Three ways to change flux: change B, A, or angle
Lessons 13–14

Faraday's and Lenz's Laws

  • Faraday: $\varepsilon = -N \Delta\Phi/\Delta t$
  • Lenz: induced current opposes the change
  • Conservation of energy requires opposition
Lessons 15, 19, 20 and 11

Induction Applications, Transformers, Grid and Generators

  • $V_p/V_s = N_p/N_s$
  • Ideal transformer: $P_p = P_s$
  • Need a changing flux: steady DC gives no sustained secondary emf
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Essential Formulae, Electromagnetic Induction

$\Phi = BA \cos \theta$Magnetic flux (Wb)
$\varepsilon = -N \dfrac{\Delta \Phi}{\Delta t}$Faraday's Law
$\varepsilon_0 = NBA\omega$Peak emf in AC generator
$\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$Transformer turns ratio
$P_{loss} = I^2 R$Power loss in transmission
Key Terms
Magnetic fluxAmount of magnetic field through an area: Phi = BA cos theta
Faraday's LawInduced emf equals rate of change of flux linkage
Lenz's LawInduced current opposes the change in flux that produced it
Slip ringsContinuous contacts for rotating coil; no current reversal
TransformerDevice using mutual induction to change AC voltage
Eddy currentInduced circular current in a conductor by changing flux
Multiple Choice, 10 Questions

1. A coil of 200 turns experiences a flux change from 0.020 Wb to 0.060 Wb in 0.20 s. The average induced emf is:

A20 V
B40 V ($\varepsilon = 200 \times 0.040/0.20$)
C80 V
D400 V

2. Lenz's Law is a consequence of:

ANewton's Third Law
BConservation of energy
CCoulomb's Law
DOhm's Law

3. The emf in an AC generator is maximum when the coil is:

APerpendicular to the magnetic field
BParallel to the magnetic field
CAt 45 degrees to the field
DStationary

4. A transformer has Np = 200 and Ns = 800. If Vp = 50 V, Vs is:

A12.5 V
B200 V ($V_s = 50 \times 800/200$)
C100 V
D400 V

5. A transformer gives no sustained secondary emf on steady DC because:

ADC produces too much heat
BSteady DC produces constant flux, so no emf is induced
CAC has higher voltage
DAC can travel farther

6. A magnet is dropped through a copper tube. It falls slower than in air because:

ACopper is magnetic
BEddy currents create an opposing magnetic field
CAir resistance is greater
DThe magnet loses magnetism

7. The peak emf of an AC generator with n = 100, B = 0.50 T, A = 2.0x10^-3 m², omega = 50 rad/s is:

A2.5 V
B5.0 V ($\varepsilon_0 = 100 \times 0.50 \times 2.0\times10^{-3} \times 50$)
C10 V
D25 V

8. To increase the emf induced in a coil, you could:

ADecrease the number of turns
BIncrease the rate of flux change
CKeep flux constant at a high value
DIncrease the time for flux change

9. An ideal step-up transformer has Vp = 100 V, Vs = 400 V, and Ip = 2.0 A. Is is:

A0.50 A ($I_s = V_p I_p / V_s = 200/400$)
B2.0 A
C4.0 A
D8.0 A

10. A north pole approaches a loop. The induced current creates a magnetic field that:

ARepels the approaching magnet
BAttracts the approaching magnet
CIs parallel to the magnet's field
DHas no effect
Short Answer, 2 Questions

1. (4 marks) A coil with 60 turns experiences a flux change from 0.030 Wb to 0.070 Wb.

  • Calculate the average induced emf if the change takes 0.20 s. (2 marks)
  • If the same flux change occurs in 0.050 s, calculate the new emf and explain why it is larger. (2 marks)

2. (4 marks) A transformer has 400 primary turns and 1200 secondary turns. The primary is connected to 230 V AC.

  • Calculate the secondary voltage. (1 mark)
  • Is this a step-up or step-down transformer? (1 mark)
  • Explain why this transformer gives no sustained output when connected to a steady DC battery. (2 marks)
Answers

Multiple Choice: 1-B, 2-B, 3-B, 4-B, 5-B, 6-B, 7-B, 8-B, 9-A, 10-A

Short Answer 1: (a) epsilon = 60 x (0.070-0.030)/0.20 = 60 x 0.040/0.20 = 12 V. (b) epsilon = 60 x 0.040/0.050 = 48 V. The emf is larger because the rate of change of flux is greater. Faraday's Law states emf is proportional to the rate of change of flux, not the total change.

Short Answer 2: (a) Vs = 230 x 1200/400 = 690 V. (b) Step-up (Vs > Vp). (c) Steady DC after the switching transient produces constant current and flux, so there is no continuing induced secondary emf. Switching or pulsed DC can change flux, but ordinary transformer operation requires a continuously changing input.