understand and explain experiments that demonstrate: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the induced e.m.f. is in such a direction as to oppose the change producing it • the factors affecting the magnitude of the

Published by Patrick Mutisya · 14 days ago

Cambridge A-Level Physics 9702 – Electromagnetic Induction Notes

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic flux through a closed circuit induces an electromotive force (e.m.f.) in that circuit. The phenomenon underpins the operation of generators, transformers and many modern devices.

Key Concepts

  • Magnetic flux, \$\Phi_B = BA\cos\theta\$, where \$B\$ is magnetic field strength, \$A\$ the area of the loop and \$\theta\$ the angle between \$B\$ and the normal to the loop.
  • Faraday’s law: \$\mathcal{E} = -\frac{d\Phi_B}{dt}\$

    • The negative sign expresses Lenz’s law – the induced e.m.f. acts to oppose the change in flux.

  • Lenz’s law: The direction of the induced current is such that its own magnetic field opposes the original change in flux.

Experiment 1 – Moving a Magnet Through a Coil (Changing Flux)

This classic experiment shows that a varying magnetic flux induces an e.m.f. in a stationary circuit.

ApparatusProcedureObservations
Coiled wire (≈ 100 turns), galvanometer, bar magnet, wooden stand.

  1. Connect the coil to the galvanometer.
  2. Insert the magnet into the coil at a constant speed and note the galvanometer deflection.
  3. Repeat while withdrawing the magnet.
  4. Vary the speed of insertion/withdrawal.

  • Deflection occurs only while the magnet is moving.
  • Direction of deflection reverses when the magnet is withdrawn.
  • Greater speed → larger deflection (greater e.m.f.).

Suggested diagram: Bar magnet moving through a coil connected to a galvanometer, showing direction of motion and induced current.

Experiment 2 – Rotating Coil in a Uniform Magnetic Field (Generator)

This set‑up demonstrates a continuously changing flux and allows quantitative study of the factors affecting induced e.m.f.

ApparatusProcedureKey Results
Square coil (N turns), wooden frame, strong horseshoe magnet, motor (to rotate coil), voltmeter.

  1. Mount the coil on the motor shaft so it can rotate within the gap of the magnet.
  2. Connect the coil leads to the voltmeter.
  3. Start the motor at low speed; record the peak voltage.
  4. Increase the motor speed and record the new peak voltage.
  5. Repeat with different numbers of turns (N) and different coil areas (A).

  • Peak e.m.f. \$\mathcal{E}_{\text{max}} = NAB\omega\$, where \$\omega\$ is angular speed.
  • Voltage is proportional to speed, number of turns, coil area and magnetic field strength.

Suggested diagram: Rotating rectangular coil between the poles of a horseshoe magnet, with connections to a voltmeter.

Experiment 3 – Lenz’s Law Demonstration (Opposing the Change)

Two common demonstrations illustrate the direction of the induced e.m.f. and its opposition to the cause.

  1. Falling Magnet Through a Conducting Ring

    • Drop a strong magnet through a vertical copper ring attached to a spring balance.
    • Observe that the magnet falls more slowly than in free fall.
    • Explanation: The falling magnet changes the magnetic flux through the ring, inducing a current whose magnetic field opposes the magnet’s motion (Lenz’s law).

  2. Current‑Carrying Loop Near a Magnet

    • Place a rectangular coil on a frictionless air track near a fixed magnet.
    • Pass a current through the coil and release it.
    • The coil moves away from the magnet, showing that the induced magnetic force opposes the motion that would increase flux.

Suggested diagram: Magnet falling through a conducting ring with arrows indicating induced current direction and magnetic field opposing motion.

Factors Affecting the Magnitude of the Induced e.m.f.

From Faraday’s law, the magnitude of the induced e.m.f. depends on how rapidly the magnetic flux changes. The main experimental variables are summarised below.

FactorHow it Influences \$\mathcal{E}\$Experimental Control
Rate of change of magnetic field (\$\frac{dB}{dt}\$)Higher \$dB/dt\$ → larger \$\mathcal{E}\$Move magnet faster; use stronger magnets.
Area of the loop (A)Flux \$\Phi_B = BA\cos\theta\$; larger area gives larger change in flux.Use larger coils or increase coil dimensions.
Number of turns (N)Induced e.m.f. is proportional to N (multiple loops add their e.m.f.).Wind more turns onto the same core.
Angle between field and loop normal (\$\theta\$)Flux varies as \$\cos\theta\$; rotating the coil changes flux sinusoidally.Rotate coil at different angular speeds.
Electrical resistance of the circuit (R)Higher R reduces the induced current \$I = \mathcal{E}/R\$, but does not change \$\mathcal{E}\$ itself.Insert resistors to observe current change while \$\mathcal{E}\$ remains constant.

Summary of Key Points

  • A changing magnetic flux through a closed circuit induces an e.m.f. (Faraday’s law).
  • The induced e.m.f. always acts to oppose the change that produced it (Lenz’s law).
  • The magnitude of the induced e.m.f. increases with:

    • Faster change of flux (higher speed of magnet or coil rotation).
    • Greater magnetic field strength.
    • Larger loop area.
    • More turns in the coil.

  • Experimental setups such as a moving magnet through a coil, a rotating coil in a uniform field, and falling‑magnet demonstrations provide clear, observable evidence of these principles.