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Movement Sensors

Key idea: Explain how movement sensors use changing flux linkage to induce an e.m.f., and how signal size depends on the rate of change (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. Movement sensor (induction idea)

A movement sensor can detect motion by converting a changing magnetic flux linkage into an electrical signal using Faraday’s law.

2. Key Ideas (What Earns Marks)

  • Motion can change flux linkage NΦ by changing B, A, or orientation θ.
  • Changing flux linkage induces an e.m.f.: ε = -d(NΦ)/dt
  • The induced signal can be processed and recorded to measure movement patterns.
Scope note

This is an application of electromagnetic induction (18f). Keep the explanation focused on changing flux linkage → induced e.m.f.

3. Detailed Explanations

A. A typical mechanism (qualitative)

If a coil moves in a magnetic field (or a magnet moves relative to a coil), flux linkage changes with time. This produces an induced e.m.f. that can be measured and related to the motion.

4. Common Mistakes

  • Saying “motion causes current” without mentioning changing flux linkage.
  • Forgetting that you need a closed circuit for an induced current (an induced e.m.f. can exist even if the circuit is open).

5. Exam Tips

  • Use the chain: motion → change in NΦ → induced ε → measurable signal.

6. Worked Examples

Modelled example 1

Open circuit vs closed circuit

Core

Problem

A coil moves in a magnetic field while its circuit is open. Is an induced e.m.f., an induced current, or both produced?
Study the worked solution

  1. Apply Faraday's law

    Method

    A changing flux linkage produces an induced e.m.f.

    Reason

    The law relates e.m.f. to the rate of flux-linkage change and does not require a closed conducting loop.

    Working

    E = -d(NΦ)/dt

  2. Apply the circuit condition

    Method

    No induced current flows.

    Reason

    The open circuit has no complete path for charge flow.

    Working

    open circuit ⇒ I = 0

Guided practice 2

Find induced e.m.f. magnitude from a flux change

About 4 min

Problem

A sensor coil’s flux linkage changes from 0.012 Wb turn to 0.006 Wb turn in 0.020 s. Estimate the induced e.m.f. magnitude.

Try this before viewing the solution

Unit: V

Hints

Hint 1: subtract final and initial linkage
The signed change is 0.006-0.012 = -0.006 Wb turn; take magnitude after dividing by time.
View solution step by step

  1. Find the linkage change

    Method

    Δ(NΦ) = -0.006 Wb turn.

    Reason

    Change is final minus initial.

    Working

    0.006-0.012 = -0.006 Wb turn

  2. Calculate e.m.f. magnitude

    Method

    |E| = 0.30 V.

    Reason

    Average e.m.f. magnitude is the magnitude of linkage change per unit time.

    Working

    |E| = |(-0.006)/0.020| = 0.30 V

Common misconception 3

Effect of doubling turns

Find and correct the mistake

Learner claim

A sensor coil’s turns are doubled while its motion and flux per turn stay unchanged. A learner says the induced e.m.f. is unchanged because each turn sees the same flux. Diagnose the claim.

Try this before viewing the solution

Induced e.m.f. factor

View solution step by step

  1. Identify the linked quantity

    Method

    Faraday’s law uses NΦ.

    Reason

    Every linked turn contributes to the total flux linkage.

    Working

    flux linkage = NΦ

  2. Apply the redesign

    Method

    Doubling N doubles NΦ and its rate of change for the same motion.

    Reason

    The per-turn flux history is unchanged but occurs across twice as many turns.

    Working

    N → 2N ⇒ d(NΦ)/dt → 2d(NΦ)/dt

  3. Infer the signal

    Method

    The induced e.m.f. magnitude doubles.

    Reason

    Its magnitude equals the rate of change of total linkage.

    Working

    |E| → 2|E|

Examiner practice 4

Faster change

3 marks

Examination question

The same -0.006 Wb turn flux-linkage change now occurs in 0.010 s instead of 0.020 s. Find the new induced e.m.f. magnitude and state the factor change. [3 marks]

Try this before viewing the solution

Unit: V

View solution step by step

  1. Calculate the new rate

    2 marks

    Method

    |E| = 0.60 V.

    Reason

    The same linkage change occurs over half the time.

    Working

    |E| = |(-0.006)/0.010| = 0.60 V

  2. State the comparison

    1 mark

    Method

    The e.m.f. magnitude doubles.

    Reason

    0.60/0.30 = 2.

    Working

    |E₂|/|E₁| = 2

Challenge 5

Direction sign

Minimal support

Independent transfer

The sensor motion reverses so that flux linkage increases instead of decreasing, at the same rate magnitude. What happens to the induced e.m.f. sign and polarity?

Try this before viewing the solution

Polarity change

Hints

Hint 1: retain Faraday's minus sign
Compare -d(NΦ)/dt before and after the linkage-change sign reverses.
View solution step by step

  1. Reverse the linkage-change sign

    Method

    d(NΦ)/dt changes sign but not magnitude.

    Reason

    The motion is reversed while its speed and geometry otherwise remain the same.

    Working

    d(NΦ)/dt → -d(NΦ)/dt

  2. Apply Faraday–Lenz law

    Method

    The induced e.m.f. sign reverses.

    Reason

    E = -d(NΦ)/dt changes sign when its derivative changes sign.

    Working

    E → -E

  3. Interpret the signal

    Method

    The sensor’s output polarity or current direction in a closed circuit reverses.

    Reason

    The sign change represents the opposite induced direction.

    Working

    output direction reverses

7. Mind Stretchers

Mind stretcher 1: Faster motionExtension

Explain why faster motion often produces a larger sensor signal.

Show Answer

Faster motion usually increases the rate of change of flux linkage |d(NΦ)/dt|, so the induced e.m.f. magnitude increases.

Mind stretcher 2: Improving sensitivityExtension

Suggest two design changes that would make a movement sensor produce a larger signal for the same motion.

Show Answer

Examples (any two):

  • Increase the number of turns N.
  • Use a stronger magnetic field (stronger magnet or better core).
  • Increase coil area A.
  • Arrange geometry so flux linkage changes more per unit displacement.

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