AQA A-Level Physics Paper 2, June 2023: Question 22

1 mark · Medium difficulty · Multiple Choice

Identify the graph representing the induced emf in a coil as a function of time given the variation of magnetic flux with time.

Practise this question

Question

Question 22 presents a graph of magnetic flux φ against time t. The flux is zero up to t1, increases linearly at a steep rate between t1 and t2, remains constant at a maximum value between t2 and t3, and decreases linearly at a gentler rate back to zero between t3 and t4. Four candidate graphs (A, B, C, D) of induced electromotive force ε against time t are shown. Graph A shows a tall positive rectangular pulse from t1 to t2, zero from t2 to t3, and a shorter negative rectangular pulse from t3 to t4.
Question text

22 The magnetic flux ϕ in a coil varies with time t as shown.

Which graph shows how the emf ε induced in the coil varies with t?

[1 mark]

A

B

C

D

Mark scheme

Show the mark scheme Mark scheme for question 22 indicating the correct answer is option A, accompanied by the graph showing a tall positive rectangular pulse between t1 and t2 and a lower-magnitude negative rectangular pulse between t3 and t4.

22 A

How to answer it

Electromagnetic Induction: Induced EMF vs Time Graphs

📌 What this question tests

This multiple-choice question assesses your ability to apply Faraday's Law and Lenz's Law to deduce how induced electromotive force (emf, ε) changes over time from a magnetic flux (Φ) against time (t) graph.

  • Understanding that magnitude of induced emf is proportional to the rate of change of magnetic flux: |ε| = N(ΔΦ/Δt) = gradient of Φ-t graph .
  • Applying Lenz's law / direction of emf: opposite gradients produce emfs of opposite signs.
  • Relating time duration to magnitude: a steeper slope (shorter time interval) produces a greater magnitude of emf.

Question 22 (Multiple Choice)

Identifying the correct induced emf (ε) versus time (t) graph

✅ Correct Answer

Option A

Between t₁ and t₂, the flux gradient is positive, constant, and steep, giving a constant emf of one sign. Between t₂ and t₃, flux is constant (gradient = 0), so emf = 0. Between t₃ and t₄, the flux gradient is negative, constant, and shallower (longer time interval), giving a constant emf of the opposite sign with a smaller amplitude.

Mark allocation: [1 Mark] awarded for selecting A only.

💡 Key Knowledge

  • Faraday's Law: The magnitude of induced emf is directly proportional to the rate of change of magnetic flux linkage:
    ε = -N(ΔΦ/Δt) .
  • Gradient Link:
    • Straight line on Φ-t graph → constant gradient → constant (horizontal) value of ε.
    • Flat horizontal line on Φ-t graph → gradient = 0 → ε = 0.
  • Opposing Signs: A positive slope produces an emf of opposite polarity to a negative slope.

📐 Step-by-Step Graph Analysis

Time Interval Flux Gradient (ΔΦ/Δt) Induced EMF (ε) Graph Appearance
0 to t₁ Zero (flux is zero and flat) ε = 0 Line on the zero axis.
t₁ to t₂ Positive and constant; steep gradient because interval (t₂ - t₁) is short. Constant value (conventionally drawn as positive in this question's answer options). Rectangular block above zero axis. Height is relatively large.
t₂ to t₃ Zero (flux is constant at peak value). ε = 0 Line on the zero axis.
t₃ to t₄ Negative and constant; shallower gradient because (t₄ - t₃) > (t₂ - t₁). Constant value, opposite sign to interval (t₁ to t₂), smaller magnitude. Rectangular block below zero axis. Height is smaller than the first pulse.

❌ Common Errors & Pitfalls

  • Selecting C: Mistaking the value of flux for rate of change. Students who choose C think a triangular profile in Φ produces a triangular profile in ε. Since the slope is linear, the derivative is flat (step-function), not triangular!
  • Selecting B: Forgetting that reversing the direction of flux change (increasing vs decreasing) reverses the direction (polarity) of the induced emf.
  • Selecting D: Combining both mistakes—assuming triangular pulses and failing to show opposite polarities.
  • Ignoring pulse height: Overlooking that (t₄ - t₃) is wider than (t₂ - t₁). Because flux change ΔΦ is the same in magnitude, ΔΦ/Δt must be smaller during the longer interval, meaning the second pulse must have a lower amplitude.

🧠 Exam Technique & Elimination Strategy

  • Step 1: Check gradient type. Linear slopes on a Φ-t graph mean gradient is constant, so ε must be constant during changes. Immediately eliminate C and D.
  • Step 2: Check polarity. Flux increases first, then decreases. The gradients have opposite signs, so the induced emf must switch sides of the time axis. Eliminate B.
  • Step 3: Confirm with amplitude. Option A correctly displays a taller, narrower positive pulse followed by a shorter, wider negative pulse. This matches the conservation of flux ( Area under ε-t = ΔΦ ).

Topics

Physics · Practical skills · 3.7 Fields and their consequences (A-level only) · Data analysis

Question and mark scheme from the AQA A-Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.