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Subway Braking System

Key idea: Explain electromagnetic (eddy current) braking: motion in a magnetic field induces currents that oppose motion, producing a retarding force (A Level Physics).

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Use magnetic flux and flux-linkage relationships.
  • Apply Faraday's and Lenz's laws to induced e.m.f. and direction.
  • Explain simple applications of electromagnetic induction, including motional e.m.f. and eddy currents.
  • Explain simple iron-core transformer operation and apply ideal transformer ratios.

1. Definitions (Must Know)

A. Eddy current braking (idea)

Eddy current braking uses electromagnetic induction to produce a retarding force on a moving conductor in a magnetic field.

2. Key Ideas (What Earns Marks)

  • Motion causes changing flux in a conductor → induced e.m.f. → eddy currents.
  • By Lenz’s law, eddy currents produce effects that oppose the change (oppose the motion), giving a retarding force.
  • Braking effect weakens as speed decreases because the rate of change of flux decreases.
Scope note

This is a qualitative induction application (18f). For exam explanations, focus on the cause-and-effect chain.

3. Detailed Explanations

A. Step-by-step chain for rail braking

  1. An electromagnet near the rail produces a magnetic field.
  2. As the train moves, the rail/conductor experiences changing flux.
  3. Eddy currents are induced in the rail.
  4. The magnetic effect of the eddy currents opposes the change, producing a retarding force.
  5. As the train slows, induced currents reduce, so braking smoothly decreases.

4. Common Mistakes

  • Saying “eddy currents oppose the magnetic field” (they oppose the change / motion that changes the flux).
  • Forgetting the braking effect depends on speed (rate of change).

5. Exam Tips

  • Use the words “changing flux” and “Lenz’s law” explicitly for explanation marks.

6. Worked Examples

Modelled example 1

Why does braking fade at low speed?

Core

Problem

Explain why eddy-current braking becomes weaker as the vehicle slows down.
Study the worked solution

  1. Compare flux-change rates

    Method

    Slower relative motion gives a smaller rate of change of magnetic flux through the conductor.

    Reason

    The conductor crosses the field variation less rapidly.

    Working

    v↓ ⇒ |dΦ/dt|↓

  2. Apply Faraday's law

    Method

    The induced e.m.f. and eddy-current magnitude decrease.

    Reason

    A smaller flux-change rate produces a smaller induced e.m.f., which drives less current.

    Working

    |E|↓ ⇒ I_eddy↓

  3. Apply Lenz's law

    Method

    The opposing magnetic effect and retarding force become weaker.

    Reason

    The smaller eddy currents produce a smaller magnetic interaction opposing the motion.

    Working

    I_eddy↓ ⇒ F_brake↓

Guided practice 2

Why does it not work at rest?

About 4 min

Problem

Explain why eddy-current braking is ineffective when the train is stationary.

Try this before viewing the solution

Quantity that becomes zero

Hints

Hint 1: separate field from flux change
The electromagnet’s field may still be present; ask whether a stationary rail section experiences changing flux.
View solution step by step

  1. Apply the motion condition

    Method

    At rest there is no relative motion between the field pattern and conductor.

    Reason

    The train is stationary in the stated setup.

    Working

    v = 0

  2. Test for induction

    Method

    The conductor’s flux is not changing, so induced e.m.f. and eddy currents are negligible.

    Reason

    Faraday’s law requires a changing flux.

    Working

    dΦ/dt = 0 ⇒ E ≈ 0 ⇒ I_eddy ≈ 0

  3. Infer the braking force

    Method

    The electromagnetic braking force is negligible.

    Reason

    There is no appreciable induced current to create the opposing magnetic interaction.

    Working

    I_eddy ≈ 0 ⇒ F_brake ≈ 0

Common misconception 3

Slotted conductor

Find and correct the mistake

Learner claim

Some braking discs have slots. A learner says the extra metal edges make eddy-current braking stronger. Diagnose the claim.

Try this before viewing the solution

Effect of slots

View solution step by step

  1. Inspect the current paths

    Method

    Slots interrupt large closed eddy-current loops.

    Reason

    Induced circulating currents cannot cross the insulating gaps.

    Working

    slots ⇒ smaller or broken loops

  2. Compare current

    Method

    The effective path resistance rises and eddy-current magnitude falls.

    Reason

    The available conducting loops are more restricted.

    Working

    Rₚₐₜₕ↑ ⇒ I_eddy↓

  3. Correct the braking claim

    Method

    Slots reduce the retarding force.

    Reason

    Smaller eddy currents create a weaker opposing magnetic effect.

    Working

    I_eddy↓ ⇒ F_brake↓

Examiner practice 4

Where does the energy go?

3 marks

Examination question

During eddy-current braking, explain what happens to the train’s kinetic energy and identify where the transferred energy is dissipated. [3 marks]

Try this before viewing the solution

View solution step by step

  1. Identify the mechanical change

    1 mark

    Method

    The train’s kinetic energy decreases.

    Reason

    The retarding force does negative work on the moving train.

    Working

    Δ Eₖ < 0

  2. Identify the receiving store

    1 mark

    Method

    Energy is transferred mainly to internal energy of the conductor or rail.

    Reason

    The induced currents flow through material with resistance.

    Working

    Eₖ → Eᵢₙₜₑᵣₙₐₗ

  3. Name the mechanism

    1 mark

    Method

    The energy is dissipated as thermal heating by eddy-current I²R losses.

    Reason

    Electrical resistance converts the induced-current energy into heating.

    Working

    Pₜₕₑᵣₘₐₗ = I_eddy^(,2)R

Challenge 5

Speed scaling (qualitative)

Minimal support

Independent transfer

If the train’s speed increases, how does the braking effect change qualitatively, and why?

Try this before viewing the solution

Braking effect at higher speed

Hints

Hint 1: reverse the low-speed chain
Start with how quickly the moving conductor experiences a flux change at higher speed.
View solution step by step

  1. Increase the flux-change rate

    Method

    Higher speed generally increases the magnitude of the flux-change rate.

    Reason

    The conductor moves through the magnetic-field variation more rapidly.

    Working

    v↑ ⇒ |dΦ/dt|↑

  2. Increase induced current

    Method

    The induced e.m.f. and eddy-current magnitude increase.

    Reason

    Faraday’s law links e.m.f. to flux-change rate.

    Working

    |E|↑ ⇒ I_eddy↑

  3. Infer the retarding effect

    Method

    The braking effect becomes stronger, until practical limits matter.

    Reason

    Larger eddy currents produce a stronger magnetic effect opposing the motion.

    Working

    I_eddy↑ ⇒ F_brake↑

7. Mind Stretchers

Mind stretcher 1: Non-conducting railsExtension

What would happen to eddy-current braking if the rail were a good electrical insulator? Explain.

Show Answer

An insulator does not allow charge to move freely, so large eddy currents cannot form.

With negligible eddy currents, the opposing magnetic braking effect would be much weaker.

Mind stretcher 2: Heating trade-offExtension

Why can “stronger” eddy-current braking also create an engineering problem?

Show Answer

Stronger braking means larger eddy currents, which increases I²R heating.

Excessive heating can damage components or require cooling/thermal design, so braking strength must be balanced with temperature limits.

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027