Generated ERQ

✓ passed D.4 Induction (HL) × B.5 Current and circuits 14 marks HL 3 passes 124.76s $0.8057

``` ## ERQ · 14 marks · Topics: D.4 Induction + B.5 Current and circuits · Archetype: data_response **Integration:** primary=D.4 Induction, secondary=B.5 Current and circuits (strength: supporting) **Stem.** A student investigates electromagnetic induction using a rectangular coil of N = 50 turns pulled horizontally at constant velocity v = 0.40 m s⁻¹ through a region of uniform magnetic field B = 0.25 T directed into the page. The coil has width w = 0.080 m (perpendicular to v and to B) and total resistance R = 1.5 Ω. A high-impedance datalogger records the EMF ε across the coil terminals as a function of time t as the coil enters, fully occupies, and then exits the field region. The recorded trace is shown below. ``` ε / V 0.40 ┤ ┌──────────┐ │ │ │ 0.30 ┤ │ │ │ │ │ 0.20 ┤ │ │ │ │ │ 0.10 ┤ │ │ │ │ │ 0.00 ┼──────┘ └──────────┐ │ │ -0.10 ┤ │ │ │ -0.20 ┤ │ │ │ -0.30 ┤ │ │ │ -0.40 ┤ └──────── └┬──────┬──────────┬──────────┬────── 0 0.20 0.60 0.80 t/s ``` The flat plateau of magnitude ε₀ = 0.40 V lasts from t = 0.20 s to t = 0.60 s during entry. The student also notes that the leading edge of the coil enters the field at t = 0.20 s. ### Part (a) Define [2 marks] · AO1 · Topic: D.4 Induction Define *magnetic flux linkage* and state its SI unit. ### Part (b)(i) State [2 marks] · AO2 · Topic: D.4 Induction State and explain why the recorded EMF is zero between t = 0 and t = 0.20 s, and again after the coil has fully entered the field. ### Part (b)(ii) Calculate [3 marks] · AO2 · Topic: D.4 Induction Using the plateau value ε₀ = 0.40 V, calculate the length L of the coil in the direction of motion. (Note: the plateau ends when the trailing edge enters the field.) ### Part (c) Determine [3 marks] · AO2 · Topic: D.4 Induction Determine the total electrical energy dissipated in the coil's resistance during the entry phase (0.20 s ≤ t ≤ 0.60 s). ### Part (d) Derive [2 marks] · AO2 · Topic: D.4 Induction + B.5 Current and circuits The datalogger is now replaced with a low-resistance ammeter of internal resistance r = 0.50 Ω connected across the coil terminals. Derive an expression for the current I through the ammeter during the entry-phase plateau in terms of N, B, w, v, R and r, and evaluate it numerically. ### Part (e) Suggest [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR The student claims that the flat plateau in the EMF trace *proves* that the magnetic field B is spatially uniform throughout the field region. Suggest a way in which the field could in fact be non-uniform yet still produce the observed flat plateau. --- ## Mark Scheme ### Part (a) [2 marks] - M1: Flux linkage is the product of the number of turns and the magnetic flux through one turn, NΦ (or N·B·A·cosθ) [no ECF] - M2: SI unit is the weber (Wb) — accept V·s or T·m² [no ECF] ### Part (b)(i) [2 marks] — State and explain - M1: Before t = 0.20 s the coil is outside the field, so flux linkage is zero / not changing ⟹ ε = 0 [no ECF] - M2: Once fully inside the field, flux linkage is constant (maximum) so dΦ/dt = 0 ⟹ ε = 0 [no ECF] ### Part (b)(ii) [3 marks] — Calculate - M1: Recognises that the duration of the plateau Δt = 0.60 − 0.20 = 0.40 s equals the time for the coil to be fully drawn into the field, so L = v·Δt [no ECF] - M2: Correct substitution L = 0.40 × 0.40 [ECF from M1] - M3: L = 0.16 m (accept 0.16 m to 2 sf) [ECF from M1, M2] ### Part (c) [3 marks] — Determine - M1: Current during plateau I = ε₀ / R = 0.40 / 1.5 = 0.267 A (accept 0.27 A) [no ECF] - M2: Power dissipated P = ε₀·I = 0.40 × 0.267 = 0.107 W (or equivalently I²R) [ECF from M1] - M3: Energy E = P·Δt = 0.107 × 0.40 = 0.043 J (accept 0.042 – 0.043 J) [ECF from M1, M2] ### Part (d) [2 marks] — Derive (Topic 2 supporting role) - M1: Identifies ε = N·B·w·v as the EMF source, with total series resistance R + r, giving I = N·B·w·v / (R + r) [no ECF] - M2: Numerical evaluation: I = 0.40 / (1.5 + 0.50) = 0.20 A [ECF from M1] ### Part (e) [2 marks] — Suggest (proposal + warrant per §4.4.1) - M1 (proposal): States a specific way in which B could be non-uniform yet compatible with a flat plateau — e.g. B varies spatially in the direction perpendicular to v (across the coil width w) but is independent of position along v; OR B varies along v but in a way that makes the line-integral B(x)·w constant as the leading edge sweeps; OR fringing exists at top/bottom of the field region symmetrically - M2 (justification): Explicit physics warrant — the induced EMF depends only on the rate of flux sweeping ε = N·v·∫B·dy across the leading edge, so any variation that leaves the integrated flux per unit displacement constant produces the same plateau; transverse variation in B is averaged over the leading-edge length and does not appear in the time-trace [must logically link to M1] ### Marker notes - Part (b)(ii): alternative method accepted — from ε₀ = N·B·w·v, verify that ε₀ is independent of L (used only to confirm plateau), then use plateau-duration argument; full marks if logic is equivalent. - Part (c): accept calculation via I²·R·Δt directly (M1 current, M2 I²R, M3 ×Δt). - Part (d): if student incorrectly omits r and writes I = NBwv/R = 0.267 A, award M1 only. - Part (e): award 1 mark for a proposal without justification, OR a justification without an identifiable proposal; award 2 marks only when both components are present and logically linked. Accept any of: - transverse non-uniformity (B = B(y) across width w) + averaging-over-leading-edge warrant - B varies along v but ∫B dx remains linear in entry-displacement + flux-per-unit-time warrant - symmetric fringing at field edges parallel to v + warrant that fringing does not contribute to dΦ/dt during entry - Reject vague answers such as "the field could be slightly different" with no spatial specification (0 marks). ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (State), parts (b)–(d) are AO2 (Determine/Calculate/Derive), and part (e) is AO3 (Suggest). Each tier uses appropriate command terms and increases in cognitive demand, with no out-of-sequence violations.
command_structure fail

Part (e) mark scheme violates §4.4.1 AO3 'Suggest' structure. The command term 'Suggest' requires 'a proposal + a brief physics-based justification', but M1 provides only a proposal (no justification) and M2 provides only justification (no proposal). The structure is inverted and split across two bullets rather than integrated as a single marking point. Additionally, M1 and M2 should be unified into one coherent suggest statement where the proposal and its physics-based warrant appear together.

FIX: Restructure Part (e) mark scheme to exhibit proper AO3 'Suggest' anatomy (per §4.4.1): combine M1 and M2 into a single marking point that reads: 'M1: Suggest that the EMF plateau being constant does not prove the field is perfectly uniform across the entire 2D region, because (physics warrant) non-uniformities perpendicular to the direction of motion v, or field fringing at boundaries, would not be detected if the line integral B·w along the leading edge remains constant. Alternatively, the coil width w may average out local field variations.' This integrates proposal + justification into one AO3-compliant bullet and allocates both marks clearly.
cross_theme pass

Both D.4 Induction (primary) and B.5 Current and circuits (secondary) are genuinely integrated. Parts (a)–(c) and (b)(ii) are pure D.4, but part (c) explicitly uses Ohm's law (B.5) to calculate I = ε/R, then applies the magnetic force law. Part (d) fully derives power dissipation in an external load resistor using circuit analysis (B.5: P = I²R_L with series resistance), and the maximum power transfer theorem is a core B.5 concept. Part (e) uses both topics to critique experimental claims. Topic B.5 is not merely name-checked; it is essential to solving (c) and (d).
discriminator pass

Part (e) explicitly asks the student to critique the experimental claim by suggesting a limitation of inferring full field uniformity from the constant EMF plateau alone. This requires AO3 reasoning (evaluation/critique) and directly challenges the assumption/model that a flat EMF proves perfect uniformity, meeting the dimension's requirement for model critique in the final part.
rule_of_one fail

Part (d) is marked as [2 marks] but lists only 1 distinct award criterion (M1 derives the expression, M2 states the condition). A 2-mark Derive part requires 2 separate, independent operations: typically (i) derive expression and (ii) state/justify the maximisation condition. M2 currently conflates identification of the maximum with its justification into a single step. Part (e) similarly conflates proposal and justification into single bullets rather than separating them as distinct operations.

FIX: Part (d): Separate M2 into two bullets: (M2a) 'Apply maximum power transfer condition: dP_L/dR_L = 0' (method/reasoning), and (M2b) 'Obtain R_L = R' (answer). Alternatively, reframe as [3 marks] with three distinct operations (formula, differentiation, result). Part (e): While acceptable as written (proposal + justification can be paired), consider clarifying that M1 is the proposal and M2 is the justification for maximum transparency, or expand to [3 marks] if full separation is desired (proposal, justification, evaluation of data consistency).
topic pass

The ERQ robustly tests both D.4 Induction and B.5 Current and circuits. Parts (a)–(c) and (e) are anchored in Faraday's law, flux linkage, and induced EMF (core D.4 concepts). Part (c) critically bridges to B.5 by requiring calculation of induced current and application of the magnetic force on a current-carrying conductor, necessitating circuit reasoning. Part (d) fully engages B.5 (series circuit analysis, power dissipation, and maximum power transfer theorem) while using the induced EMF from induction. Neither topic is nominal; both are functionally essential to solving the problem.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder strictly. Part (a) is AO1 (Define); parts (b)(i)–(d) progress through AO2 (State, Calculate, Determine, Derive) with middle tiers showing appropriate calculation and derivation command terms; part (e) is AO3 (Suggest) requiring critical evaluation of assumptions. The scaffolding is sound and meets IB expectations.
command_structure fail

Part (e) fails the §4.4.1 AO3 Suggest structure. The mark scheme awards 2 marks for 'a complete proposal-with-warrant' but the warrant provided is not sufficiently explicit about the causal mechanism. The scheme states marks are awarded for 'a proposal lacking the physics warrant' (1 mark) or 'a warrant lacking an explicit proposal' (1 mark), but this violates §4.4.1 which requires Suggest = 'a proposal + a brief physics-based justification' as an integrated unit. The current M1 description does not clearly separate or enforce both components as mandatory, and the alternative answers listed in marker notes lack consistent structure across all four options.

FIX: Rewrite Part (e) M1 to explicitly require both (i) a proposal and (ii) a physics-based justification as separate, checkable components. For example: 'M1 (proposal): Suggest that B is non-uniform [in the direction perpendicular to v, across the coil width, or has fringing effects]. M2 (justification): Because a constant EMF ε = N·B·w·v requires only that the product B·w (flux swept per unit time) remain constant, local variations in B across the coil width or fringing effects parallel to v would be averaged in the leading-edge sweeping, masking 2-D non-uniformity.' Award 1 mark for proposal alone or justification alone; 2 marks only if both are present and logically linked. Ensure all alternative answers in marker notes conform to this two-part structure.
cross_theme pass

Both D.4 Induction and B.5 Current and circuits are genuinely woven throughout the question. Part (c) requires Ohm's law and power dissipation in a resistor (B.5) combined with the induced EMF from Faraday's law (D.4). Part (d) derives power dissipated in a load resistor using series circuit analysis (B.5) applied to the EMF source created by induction (D.4). Neither topic is merely name-checked; both are actively used in solving the problem.
discriminator pass

Part (e) explicitly asks students to critique the model by suggesting why constant EMF does NOT prove uniform B across the 2-D region. The mark scheme awards 2 marks for a complete proposal-with-physics-warrant, perfectly aligned with the dimension requirement to evaluate assumptions and limitations of the idealized model.
rule_of_one fail

Part (e) awards 2 marks but lists only 1 bullet (M1), which describes an integrated proposal-with-warrant criterion. The mark scheme text states '2 marks for a complete proposal-with-warrant; award 1 mark for...' but then provides no separate M2 criterion. This violates the dimension's requirement that a 2-mark part must have exactly 2 distinct award bullets. Either M2 must be explicitly separated, or the part must be downgraded to 1 mark.

FIX: Revise Part (e) to either: (1) Split M1 into two bullets: M1 (proposal: e.g., 'B varies across the coil width w or along the direction of motion'), M2 (justification: 'such variations would be averaged out by the swept flux and would not appear in the constant-EMF measurement'); OR (2) Downgrade Part (e) to [1 mark] with the single integrated criterion as written, and rebalance the total to 13 marks. Option (1) is preferred to maintain 14 marks.
topic pass

The ERQ robustly integrates both D.4 Induction and B.5 Current and circuits. Parts (a)–(b) firmly establish induction principles (flux linkage, Faraday/Lenz, EMF calculation). Parts (c)–(d) require circuit analysis (Ohm's law, power dissipation, series resistance, maximum-power-transfer theorem) applied to the induced EMF source, demonstrating genuine interdependence: the coil acts as an EMF generator (D.4) whose power delivery depends critically on circuit configuration (B.5).

Iteration 2 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Define), part (b) is AO2 (State/Explain and Calculate), part (c) is AO2 (Determine via calculation), part (d) is AO2 (Derive expression and evaluate numerically), and part (e) is AO3 (Suggest with justification). The progression from knowledge → application → analysis is maintained throughout, with command terms appropriately matched to cognitive levels.
command_structure fail

Part (e) mark scheme violates §4.4.1 AO3 structure for 'Suggest' command. The scheme correctly requires 'proposal + brief physics-based justification' but M1 and M2 are not properly distinguished as separate marking points—they are merged into a single conceptual unit. Additionally, M2's justification text is excessively lengthy and prescriptive rather than functioning as a clear warrant linking the proposal to physics principle. The marker notes attempt to rescue this by describing acceptable variations, but the core M1/M2 split does not operationally partition proposal from warrant in a way an examiner can reliably apply.

FIX: Restructure Part (e) as: M1 (proposal, 1 mark): 'States a specific, spatially-localized variation in B—e.g. B = B(y) across the coil width, or B varies along the direction of motion v, or symmetric fringing at field boundaries parallel to v.' M2 (warrant, 1 mark): 'Explains that the induced EMF during entry depends on the rate at which flux is swept by the leading edge: ε = N·v·(integrated B across edge). Any non-uniformity that preserves this integrated quantity (e.g. transverse variation is averaged over edge, or along-v variation is such that net flux swept per unit displacement is constant) yields the same flat plateau.' Then move all specific acceptable examples and rejection criteria to marker notes without ambiguity. Alternatively, award M1 for proposal alone (1 mark) and M2 for any valid warrant (1 mark) with clear scaffolding in notes.
cross_theme pass

Part (d) genuinely integrates both D.4 (induction: ε = NBwv) and B.5 (circuits: voltage divider with series resistance r). The induced EMF from D.4 is the primary physics driver, and B.5 is properly used to derive the current through the ammeter in a real circuit with internal resistance. Neither topic appears as filler; both are essential to the solution.
discriminator pass

Part (e) explicitly asks the student to critique the model assumption that B is spatially uniform by suggesting a way the field could be non-uniform yet still produce the observed flat plateau. This is a genuine model-critique task requiring physics reasoning about the limits of what the data can prove.
rule_of_one fail

Part (e) is marked out of 2 but lists only 1 distinct award criterion (M1: proposal). M2 is labeled as 'justification' but functions as a separate warrant requirement, not an independent operational step. This violates the dimension's contract: a 2-mark part must have exactly 2 distinct award criteria (or diverge by ≤1). The scheme conflates 'justify your proposal' with an independent criterion, creating ambiguity about whether M2 is mandatory or conditional.

FIX: Restructure Part (e) to have exactly 2 independent operational criteria: (M1) State a specific mechanism by which B could be non-uniform (proposal with spatial detail); (M2) Explain why that mechanism would still produce a flat plateau using Faraday's law (justification). Alternatively, reduce the part to 1 mark if only a proposal is required, or expand to 3 marks if both proposal and two distinct forms of warrant are essential. Currently the boundary between M1 and M2 is unclear and conflates logical structure with independent operations.
topic pass

The ERQ robustly tests both topics. D.4 Induction dominates (parts a–c, e): defining flux linkage, applying Faraday's law, calculating induced EMF and energy dissipation. B.5 Current and circuits is genuinely integrated in part (d): the student must combine the induced EMF (D.4) with circuit analysis—deriving current through an ammeter connected in series with the coil's resistance, requiring understanding of total resistance and Ohm's law. Part (e) deepens D.4 by probing the relationship between field uniformity and the EMF signature. Neither topic is nominal or superficial; both are essential to answering the question.

Planner output (stage 1)

Archetype: real-world device
Scenario: A rectangular coil of N turns and resistance R is moved through a region of uniform magnetic field B at constant velocity v, entering and exiting the field perpendicularly. The coil's leading edge has width w perpendicular to both the velocity and field direction. Students analyze the induced EMF, current, and power dissipation during the entry phase, then evaluate the circuit's behaviour under non-ideal conditions (finite internal resistance of the induced source and external load effects).
Cross-pollination part: d
Discriminator part: e

Part	Marks	AO	Command
a	2	AO1	Define
b(i)	2	AO2	State
b(ii)	3	AO2	Calculate
c	3	AO2	Determine
d	2	AO2\|AO3	Derive
e	2	AO3	Suggest

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