Generated ERQ

✓ passed D.2 Electric and magnetic fields × A.2 Forces and momentum 12 marks SL 3 passes 101.84s $0.7130

``` ## ERQ · 12 marks · Topics: D.2 Electric and magnetic fields + A.2 Forces and momentum · Archetype: theory_application **Integration:** primary=D.2 Electric and magnetic fields, secondary=A.2 Forces and momentum (strength: supporting) **Stem.** A laboratory proton accelerator produces a narrow beam for a materials-analysis experiment. Protons are released from rest near a heated filament and accelerated horizontally through a potential difference of 2.5 kV in an evacuated chamber. The accelerated protons then enter a velocity selector consisting of a region where a uniform electric field of magnitude 1200 V m⁻¹ points vertically downward, crossed with a uniform horizontal magnetic field perpendicular to the beam direction. Only protons travelling at the selected speed emerge undeflected through a narrow exit slit. The mass of a proton is 1.67 × 10⁻²⁷ kg and its charge is 1.60 × 10⁻¹⁹ C. Treat gravitational effects on the protons as negligible. ### Part (a) State [2 marks] · AO1 · Topic: D.2 State the condition on the electric force and magnetic force acting on a charged particle for it to pass undeflected through a velocity selector, and write the resulting relationship between the particle's speed v, the electric field strength E and the magnetic flux density B. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: D.2 Calculate, in joules, the kinetic energy gained by a proton accelerated from rest through the 2.5 kV potential difference. ### Part (b)(ii) Determine [2 marks] · AO2 · Topic: D.2 Determine the speed of the proton on entering the velocity selector. ### Part (c) Show that [3 marks] · AO2 · Topic: D.2 Using the speed obtained in (b)(ii) and the electric field strength of 1200 V m⁻¹, show that the magnetic flux density required for the proton to pass undeflected through the selector is approximately 1.73 × 10⁻³ T. ### Part (d) Discuss [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR · Topic: D.2+A.2 The momentum of a proton entering the velocity selector at the selected speed appears unchanged on exit. Discuss whether the proton alone constitutes an isolated system for momentum conservation in this region, identifying one assumption made in the analysis above that may not hold for a real beam of many protons. --- ## Mark Scheme ### Part (a) [2 marks] — State - M1: Electric force on the particle is equal in magnitude and opposite in direction to the magnetic force (so the net force is zero) [no ECF] - M2: Resulting condition qE = qvB ⇒ v = E/B [no ECF] ### Part (b)(i) [3 marks] — Calculate - M1: Recognises KE gained = qV with correct substitution: KE = (1.60 × 10⁻¹⁹)(2.5 × 10³) [no ECF] - M2: Correct evaluation step shown, e.g. KE = 1.60 × 2.5 × 10⁻¹⁶ J [ECF from substitution] - M3: KE = 4.0 × 10⁻¹⁶ J [ECF from (b)(i) M1] ### Part (b)(ii) [2 marks] — Determine - M1: Uses KE = ½mv² ⇒ v = √(2KE/m), substitutes v = √(2 × 4.0 × 10⁻¹⁶ / 1.67 × 10⁻²⁷) [ECF from (b)(i)] - M2: v ≈ 6.9 × 10⁵ m s⁻¹ (accept 6.92 × 10⁵ m s⁻¹) [ECF from (b)(i)] ### Part (c) [3 marks] — Show that - M1: States/uses condition v = E/B ⇒ B = E/v [no ECF] - M2: Correct substitution B = 1200 / 6.9 × 10⁵ [ECF from (b)(ii)] - M3: B = 1.74 × 10⁻³ T, consistent with the stated 1.73 × 10⁻³ T (accept 1.7–1.8 × 10⁻³ T) [ECF from (b)(ii)] ### Part (d) [2 marks] — Discuss (balanced consideration per §4.4.1) - M1 (perspective 1 — proton not isolated): The proton experiences external electric and magnetic forces from the apparatus, therefore the proton alone is NOT an isolated system; momentum is only conserved overall if the field sources (and apparatus producing them) are included in the system. - M2 (perspective 2 — limitation of the single-proton analysis): Identifies one assumption that fails for a real beam, e.g. inter-proton Coulomb repulsion is neglected (beam protons exert forces on each other so individual momenta are not preserved), OR fringe/non-uniform field regions at entry/exit are neglected, OR gravitational force on the proton has been ignored. ### Marker notes - (a): accept a clearly labelled diagram showing F_E and F_B equal and opposite as equivalent to M1. - (b)(i): full marks if answer is given as 4.0 × 10⁻¹⁶ J with one line of working. - (b)(ii): accept any speed in the range 6.9–6.93 × 10⁵ m s⁻¹. - Show-that target in (c): 1.73 × 10⁻³ T given to 3 sig figs; student-derived 1.7–1.8 × 10⁻³ T acceptable for M3. - (d) accept any one of: space-charge / Coulomb repulsion between protons in the beam; non-uniformity / fringing of E or B fields near the slits; finite beam width so not all protons travel at the selected speed; gravitational force neglected; relativistic correction neglected. - ECF applies throughout (b)(ii)→(c) for numerical chain. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) uses State/Justify (AO1), parts (b) and (c) use Calculate/Determine/Show that (AO2), and part (d) uses Explain (AO3). The progression from knowledge recall through calculation to higher-order reasoning is properly sequenced.
command_structure warning

critic parse error: Expecting ',' delimiter: line 6 column 327 (char 1073); raw: ```json { "passed": false, "severity": "fail", "reasoning": "Part (d) mark scheme violates §4.4.1 AO3 structure fo
cross_theme fail

Part (d) only names A.2 (Forces and momentum) in the ASSUMPTIONS DISCRIMINATOR label but does not genuinely integrate both concepts in the problem-solving chain. Parts (a)–(c) are entirely D.2 (electric and magnetic fields); part (d) merely applies Newton's second law to explain why the student's reasoning is flawed. A.2 concepts (momentum conservation, impulse-momentum theorem) appear only as discussion labels in the mark scheme, not as essential physics that must be worked through to answer the question. The second topic functions as decoration rather than an integrated analytical requirement.

FIX: Restructure part (d) to require students to calculate or compare the impulse from each force separately, or to explicitly derive momentum change using Δp = F_net · Δt, or to analyse the total momentum of the proton–field system. Alternatively, replace part (d) with a genuine two-concept question: e.g., 'The proton exits the selector and enters a region where only a magnetic field exists. Explain, using both concepts from D.2 and A.2, why the proton then follows a circular path and whether its momentum magnitude changes.' This would require D.2 (magnetic force calculation) and A.2 (centripetal force, circular motion dynamics) to be solved together.
discriminator pass

Part (d) explicitly asks the student to critique the student's reasoning by distinguishing between the claim that 'no forces act' versus 'the net force is zero.' This is a clear model-critique task (AO3) that requires students to evaluate an assumption and explain where the reasoning breaks down—a hallmark of the final part asking for critical evaluation rather than mere calculation.
rule_of_one fail

Part (d) has 2 marks but 3 distinct award bullets are listed in the mark scheme. M1 identifies the two forces, M2 states they are equal and opposite, and M2 also requires explanation of why momentum is conserved (net force = zero). This conflates two separable operations into a single mark bullet, violating the dimension requirement that mark count must match award-bullet count (tolerance ±1 exceeded).

FIX: Restructure Part (d) mark scheme to either: (i) split M2 into two bullets — M2 for identifying equal/opposite forces cancel to give F_net = 0, and M3 for explaining this preserves momentum (making it 3 marks total); OR (ii) consolidate to a tighter 2-mark scheme by combining M1 and M2 into a single criterion: 'identifies two equal and opposite forces (electric and magnetic) that cancel to give zero net force, preserving momentum; student's conclusion correct but reasoning incomplete because individual forces are non-zero.' This requires a corresponding adjustment to total marks or rebalancing of other parts.
topic pass

The ERQ effectively tests both D.2 (Electric and magnetic fields) and A.2 (Forces and momentum). Parts (a)–(c) require substantive application of electric and magnetic field concepts (force balance in velocity selector, field strength calculations). Part (d) explicitly bridges both topics by requiring the student to explain the relationship between net force (A.2) and momentum conservation (A.2) in the context of electric and magnetic forces (D.2), creating genuine integration rather than superficial mention.

Iteration 1 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: (a) is pure AO1 (State); (b)(i)–(c) are AO2 (Calculate/Determine/Show that); (d) is AO3 (Explain with causal reasoning integrating two topics). Command terms match cognitive levels and assessment objectives at each tier.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 Explain command-term structure. The three marking points (M1, M2, M3) do not form a coherent explicit causal chain with clear 'X therefore Y' linkage. M1 states a fact (perpendicular force), M2 introduces work/centripetal concepts without clear logical progression from M1, and M3 restates consequence without anchoring to a unified mechanism. The marker notes acknowledge the causal structure should be 'centripetal → |v| constant → |p| constant; direction changes → circular', but the scheme bullets do not reflect this necessary causal articulation.

FIX: Restructure part (d) mark scheme as an explicit causal chain: M1: 'The magnetic force F = qvB is always perpendicular to the proton's instantaneous velocity.' M2: 'Therefore, this perpendicular force does no work (W = F·d·cosθ = 0), so the kinetic energy and speed remain constant, and thus the magnitude of momentum |p| = mv remains constant.' M3: 'Because the net force is perpendicular to the momentum at each instant, the direction of momentum changes continuously (Δp = F·Δt is perpendicular to p), and this continually-changing momentum direction with constant magnitude produces uniform circular motion.' This explicitly chains: perpendicular force → zero work → constant |p| → direction changes → circular path.
cross_theme pass

The ERQ successfully integrates D.2 (Electric and magnetic fields) and A.2 (Forces and momentum) in part (d). Both concepts are genuinely used in the causal chain: D.2 establishes that the magnetic force acts perpendicular to velocity (qvB), while A.2 explains why this perpendicular force produces circular motion by keeping momentum magnitude constant but changing its direction (Δp ⊥ p). Neither topic is merely name-checked; both are essential to answering the explain question.
discriminator fail

Part (d) is framed as 'Explain... why the proton follows a circular path' and 'whether the magnitude of its momentum changes.' These are mechanism-explanation questions about the motion itself, not critiques of the model. The ERQ lacks a final part that asks the student to critique assumptions, limitations, or discrepancies (e.g., 'Suggest why real protons might deviate from circular paths', 'Discuss the assumption that the magnetic field is uniform', 'Explain a limitation of treating the proton as a point particle').

FIX: Replace or supplement part (d) with a question that explicitly requires model critique. For example: **(d) Explain... [current question as stated] [3 marks]. (e) Suggest one reason why, in practice, the proton's path might deviate from a perfect circular arc [2 marks].** Alternatively, restructure (d) as: **(d) Explain why the proton follows a circular path... Discuss one limitation of treating the proton's motion as perfectly circular in this apparatus [3 marks].** This ensures the final part explicitly addresses model assumptions or real-world deviations.
rule_of_one pass

Each part's mark allocation matches the number of distinct award criteria. Part (a): 2 marks, 2 bullets (equality + direction). Part (b)(i): 3 marks, 3 bullets (formula, evaluation, answer). Part (b)(ii): 2 marks, 2 bullets (formula/substitution, answer). Part (c): 2 marks, 2 bullets (formula application, numerical result). Part (d): 3 marks, 3 bullets (perpendicular force property, work/momentum magnitude constancy, directional change → circular motion). All allocations align within the tolerance.
topic pass

The ERQ successfully integrates both D.2 (Electric and magnetic fields) and A.2 (Forces and momentum). Parts (a)–(c) firmly test D.2 concepts (electric/magnetic force balance, kinetic energy, velocity selector physics). Part (d) is the critical integration point: it explicitly requires students to apply the perpendicular magnetic force concept (D.2) to explain circular motion AND connect this to momentum conservation and the perpendicular change in momentum direction (A.2). The mark scheme M1–M3 for part (d) enforces this two-topic causal chain, making A.2 genuinely necessary, not decorative.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly follows the cognitive ladder: Part (a) is AO1 (State), parts (b)–(c) are AO2 (Calculate/Determine/Show that), and part (d) is AO3 (Discuss). The progression from recall through calculation to evaluation is in proper order.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 structure for 'Discuss'. The two perspectives listed (M1 and M2) do not constitute a balanced two-sided discussion: M1 explains why the proton is NOT isolated (external forces), and M2 lists assumptions that fail. Neither bullet explicitly presents a contrasting perspective or trade-off. A proper 'Discuss' requires at least two substantive, competing viewpoints (e.g., 'from one perspective the proton can be treated as isolated if we neglect inter-particle effects, but from another perspective external fields make it non-isolated'). The current scheme reads as sequential explanations rather than a genuine discussion of competing positions.

FIX: Restructure Part (d) M1 and M2 to present contrasting perspectives: M1: 'From one perspective, if inter-proton Coulomb repulsion and field non-uniformity are negligible, the proton's momentum change is caused only by the external fields (E and B), and one could argue the proton's momentum is approximately conserved if the system boundary includes the apparatus.' M2: 'However, from a rigorous perspective, the proton alone cannot be an isolated system because it experiences net external forces from the apparatus fields; additionally, for a real beam, inter-proton Coulomb repulsion (or field fringing) breaks the single-particle assumption, so individual proton momenta are not truly conserved—only the total system momentum (protons + apparatus) is conserved.' This presents the required two-sided evaluation of the validity of the isolated-system assumption.
cross_theme fail

Part (d) relegates A.2 Forces and momentum to a final assumptions discussion only—the actual physics solving in (a)–(c) is entirely D.2 electric and magnetic fields. Momentum conservation is mentioned but never genuinely applied to solve the problem; A.2 concepts are name-checked as 'limitations' rather than integrated into the core analysis.

FIX: Restructure the question so that both D.2 and A.2 drive the solution. For example: (d) could ask students to apply momentum conservation explicitly—e.g. 'Using the impulse-momentum theorem, calculate the total impulse delivered by the electric and magnetic forces on a proton passing through the selector over time Δt, and explain why the exit momentum differs from the entry momentum.' Or redesign the stem to require students to analyze the trajectory of a proton using Newton's second law (A.2) in the crossed-field region before discussing the velocity-selector condition (D.2). Currently A.2 is only invoked as a caveat in assumptions, not as an active problem-solving tool.
discriminator pass

Part (d) is explicitly framed as a 'Discuss' question (AO3) requiring the student to critique the isolated-system model by identifying whether the proton alone conserves momentum AND to identify one assumption that fails for a real beam. This directly addresses model limitations and assumptions, meeting the dimension's requirement for final-part model critique.
rule_of_one fail

Part (d) is marked out of 2 but lists two distinct award criteria (M1 and M2) that together constitute a balanced discussion of perspective 1 AND perspective 2. This is structurally sound for a 2-mark Discuss question. However, the mark scheme does not clearly indicate how the 2 marks are *distributed* between these two perspectives. A strict interpretation of the dimension (mark count = number of distinct operations) would expect either (a) explicit point allocation per criterion, or (b) reframing as a single holistic mark. The current presentation risks ambiguity: if M1 and M2 are truly independent award bullets, the question appears to have 2 operations for 2 marks (acceptable), but the phrasing 'perspective 1' and 'perspective 2' suggests these are alternative pathways rather than sequential operations, which is atypical for a Calculate/Determine structure.

FIX: For Part (d), explicitly state the mark allocation, e.g. '[1 mark] M1: Explains proton is not isolated…' and '[1 mark] M2: Identifies one assumption failure (e.g. Coulomb repulsion)…' Alternatively, if both perspectives must be discussed together, reframe the question as 'Evaluate' (worth 3–4 marks) to align structure with IB mark-weighting for discussion questions. As written, the two-bullet structure for a 2-mark question is technically compliant but would benefit from explicit mark-per-bullet clarification to avoid examiner confusion.
topic pass

The ERQ genuinely integrates both topics. Parts (a)–(c) test D.2 concepts (electric field, magnetic field, velocity selector equilibrium, and magnetic flux density calculation). Part (d) is the critical integration point: it explicitly requires students to apply A.2 momentum conservation principles by evaluating whether the proton constitutes an isolated system, and demands identification of real-world assumptions (inter-proton forces, field non-uniformity) that violate the idealized single-particle analysis. Both topics are actively required, not superficial.

Planner output (stage 1)

Archetype: real-world device
Scenario: A charged particle accelerator uses crossed electric and magnetic fields to direct a beam of protons. The protons enter a region where a uniform electric field accelerates them horizontally, followed by a region of crossed perpendicular electric and magnetic fields (a velocity selector). Students must analyse the motion through each region, calculate exit velocities and deflection, and evaluate whether momentum is conserved when considering the fields as part of the system.
Cross-pollination part: d
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State the condition for a charged particle to pass undeflected through crossed electric and magnetic fields
b(i)	3	AO2	Calculate the kinetic energy gained by a proton accelerated from rest through a potential difference of 2.5 kV
b(ii)	2	AO2	Determine the velocity of the proton after acceleration
c	3	AO2\|AO3	Show that the magnetic flux density required for the velocity selector is 8.5 mT, given an electric field strength of 1200 V m⁻¹
d	2	AO3	Explain whether the momentum of the proton alone is conserved as it passes through the velocity selector, and identify what must be considered for total momentum conservation

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