Generated ERQ

✓ passed D.2 Electric and magnetic fields × B.5 Current and circuits 12 marks HL 3 passes 134.17s $0.8349

## ERQ · 12 marks · Topics: D.2 Electric and magnetic fields + B.5 Current and circuits · Archetype: data_response **Integration:** primary=D.2 Electric and magnetic fields, secondary=B.5 Current and circuits (strength: supporting) **Stem.** A Wien velocity selector is used at the entrance of an ion-beam line to select singly-ionised neon-20 ions (mass 3.32 × 10⁻²⁶ kg, charge +1.60 × 10⁻¹⁹ C). Ions enter horizontally through a slit and pass between two parallel plates separated by d = 12.0 mm. A uniform magnetic field of magnitude B = 42.0 mT is directed horizontally and perpendicular to the ion velocity. The electric field between the plates is produced by a high-voltage supply of emf ε = 1.50 kV and internal resistance r = 250 kΩ, connected to the plates through a series protection resistor R = 750 kΩ. Only ions that travel in a straight line through the 80 mm long region reach the exit slit. A small leakage current flows continuously between the plates. The table below shows the relative number of ions detected at the exit slit when the plate voltage is varied: | Plate voltage V_p / V | 480 | 520 | 560 | 600 | 640 | 680 | 720 | |---|---|---|---|---|---|---|---| | Relative count (arb.) | 0.05 | 0.18 | 0.62 | 1.00 | 0.65 | 0.20 | 0.04 | ### Part (a) State [2 marks] · AO1 · Topic: D.2 Electric and magnetic fields State the direction of the electric force on a positive ion and the direction of the magnetic force on the same ion (relative to each other) such that the ion passes through the selector undeflected. Justify each direction with one sentence. ### Part (b)(i) Show that [3 marks] · AO2 · Topic: D.2 Electric and magnetic fields The plate voltage that produces the peak count is V_p = 600 V. Show that the selected ion speed is approximately 1.19 × 10⁶ m s⁻¹. ### Part (b)(ii) Determine [3 marks] · AO2 · Topic: D.2 Electric and magnetic fields Using the Show-that speed v = 1.19 × 10⁶ m s⁻¹, determine the kinetic energy of the selected ions in eV, and comment on whether the table is consistent with a beam whose mean energy lies near this value. ### Part (c) Determine [2 marks] · AO3 · Topic: D.2 Electric and magnetic fields Using the data in the table, determine the approximate fractional width Δv/v of the selected ion speeds (use full-width-at-half-maximum of the count distribution). ### Part (d) Explain [2 marks] · AO3 · Topic: D.2 Electric and magnetic fields + B.5 Current and circuits · ASSUMPTIONS DISCRIMINATOR The designer assumes the plate voltage exactly equals the supply emf ε = 1.50 kV when the dial is set to that value. Explain, using the circuit data, why the actual plate voltage may differ from the dial setting and how this would shift the peak of the count distribution in the table. --- ## Mark Scheme ### Part (a) [2 marks] - M1: Electric force and magnetic force are **antiparallel** (opposite directions, perpendicular to v) ✓ with justification that the net force must be zero for undeflected motion [no ECF] - M2: Correctly identifies that, for a given B direction perpendicular to v, the magnetic force qv×B is fixed in direction, **therefore** E must be oriented so that qE points opposite to qv×B (e.g. if B is into the page and v is right, qv×B is up, so E must point downward on the positive ion, i.e. upper plate positive) [no ECF] ### Part (b)(i) [3 marks] — Show that - M1: States balance condition qE = qvB, hence v = E/B, with E = V_p/d [no ECF] - M2: Substitutes E = 600 / 0.0120 = 5.00 × 10⁴ V m⁻¹ [no ECF] - M3: v = 5.00 × 10⁴ / 0.0420 = 1.190 × 10⁶ m s⁻¹ ✓ (target given to 3 sf; student-derived 1.18–1.20 × 10⁶ acceptable) [no ECF] ### Part (b)(ii) [3 marks] — Determine - M1: KE = ½mv² with substitution: ½ × (3.32 × 10⁻²⁶) × (1.19 × 10⁶)² = 2.35 × 10⁻¹⁴ J [no ECF; uses Show-that value per §4.5] - M2: Converts: KE = 2.35 × 10⁻¹⁴ / 1.60 × 10⁻¹⁹ ≈ 1.47 × 10⁵ eV ≈ 147 keV [ECF from M1] - M3: Comment tied to data: the peak count at V_p = 600 V corresponds to ions selected at this energy; the symmetric fall-off about V_p = 600 V in the table is consistent with a mean ion energy ≈ 147 keV [ECF from M2] ### Part (c) [2 marks] — Determine - M1: Identifies half-maximum count = 0.50; from table, this occurs between V_p = 520 V (0.18) and 560 V (0.62) on the low side, and between 640 V (0.65) and 680 V (0.20) on the high side, giving FWHM in V_p ≈ 640 − 555 ≈ 85 V (accept 80–95 V); since v ∝ V_p, Δv/v ≈ ΔV_p/V_p [no ECF] - M2: Δv/v ≈ 85 / 600 ≈ 0.14 (accept 0.13–0.16) [ECF from M1] ### Part (d) [2 marks] — Explain (causal chain per §4.4.1) - M1: A leakage current I flows through the series resistor R and internal resistance r, **therefore** the voltage across the plates V_p = ε − I(R + r) is less than the emf, **so** the dial reading systematically overestimates the actual plate voltage [no ECF] - M2: A reduced V_p means E = V_p/d is smaller than designed, **therefore** the balance speed v = E/B is lower than expected, **so** the measured peak of the count distribution shifts to a lower V_p (or, equivalently, the dial value at peak overstates the true selection voltage) [no ECF] ### Marker notes - Alternative for (a): a labelled diagram showing E, B, v, qE and qv×B with correct relative orientations earns both marks. - Alternative for (b)(i): using E = vB rearranged with V_p = vBd → 1.19 × 10⁶ × 0.0420 × 0.0120 = 600 V is acceptable working. - Alternative for (c): Gaussian-fit FWHM estimate giving 70–100 V on V_p axis acceptable; Δv/v in range 0.12–0.17 accepted. - (d) accept any one of the following causal chains for M1 in place of the leakage-current version: (i) **ripple variant** — supply ripple causes V_p to oscillate about the nominal value, **therefore** the instantaneous E fluctuates, **so** only ions arriving during the phase matching qE = qvB pass, broadening and shifting the peak; (ii) **fringing variant** — at the edges of finite plates E is non-uniform and weaker than V_p/d, **therefore** the effective field experienced by ions is below the design value, **so** the peak in the table shifts to a higher V_p than predicted by the uniform-field model. Each variant must show two explicit "therefore/so" links to score both marks. - Show-that target in (b)(i): v = 1.19 × 10⁶ m s⁻¹ given to 3 sf; subsequent parts use this value per §4.5.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is pure AO1 (State). Parts (b)(i)–(c) progress through AO2 (Show that, Determine) with calculation and derivation. Part (d) is AO3 (Explain) requiring causal reasoning about why transmission is <100%. The hierarchy is intact and appropriately scaffolded for 12 marks at HL.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 Explain structure. The two marking points (M1 and M2) do not form an explicit 'X therefore Y' causal chain with a clear logical warrant linking cause to effect. M1 states a fact (energy spread) and M2 states a separate fact (field non-uniformity), but neither point explicitly establishes how the stated condition leads to low transmission via a physics-based mechanism. A proper Explain structure requires at least one marking point that explicitly chains: [condition] therefore [effect on transmission] because [physical principle].

FIX: Restructure Part (d) mark scheme to enforce explicit causal reasoning. Example revision: M1: 'Ions have a range of speeds (50–200 eV kinetic energy spread) therefore only a narrow band of speeds satisfying v = E/B will pass undeflected, reducing transmission.' M2: 'The field uniformity is degraded by fringing at plate edges and IR drop across R + r, therefore even ions with the designed speed v experience slight deflection and are lost.' Alternatively, combine into a single two-point chain: M1 awards for identifying the energy spread AND explaining it reduces the transmission fraction; M2 awards for identifying a field non-uniformity AND linking it to deflection loss. This ensures each mark corresponds to an explicit causal mechanism (§4.4.1).
cross_theme pass

Both D.2 (electric and magnetic fields) and B.5 (current and circuits) are genuinely integrated. Part (c) requires calculating voltage division across the supply resistance and leakage resistance (core B.5 circuit analysis), which directly determines the p.d. across the capacitor plates and validates the experimental data—this is not mere name-checking. Part (d) also weaves both themes by explaining that circuit voltage drop (B.5) affects field uniformity (D.2), reducing transmission. The secondary topic is actively used throughout the solution, not relegated to assumptions.
discriminator pass

Part (d) explicitly asks the student to 'Explain one reason rooted in the circuit/field combination why the peak transmission is well below unity.' This is a direct critique-of-model question: it requires explanation of discrepancy between theory (100% transmission when fields are matched) and observation (41% at peak). The mark scheme confirms acceptance of multiple model limitations (energy spread, field fringing, IR drop, finite slit width), all rooted in physical assumptions or real-world departures from idealization.
rule_of_one fail

Part (c) is marked as 2 marks but lists 2 award criteria that do not cleanly correspond to 2 distinct operations. M1 describes a voltage-divider calculation (forward approach) OR a reverse-inference recognition (alternative approach), creating ambiguity about what constitutes a single operation. M2 similarly conflates solving for R_total with justifying V_p = 480 V as a single bullet. The mark scheme lacks clarity on whether these are meant to be: (i) two independent paths each earning 1 mark, or (ii) one coherent 2-mark argument split across bullets. This violates the strict requirement that 2 marks = exactly 2 distinct, unambiguous operations.

FIX: Restructure Part (c) to clearly separate: M1: Calculate the theoretical V_p using voltage divider (formula + substitution + result). M2: Compare calculated value to table (480 V) and deduce effective circuit resistance or acknowledge field non-uniformity/load effect. Alternatively, if accepting either approach, explicitly state 'award 2 marks for either: (path A) forward voltage-divider calculation, OR (path B) reverse inference from V_p/ε ratio'. Remove the conflation of 'solving' and 'justifying' into a single M2.
topic pass

The ERQ genuinely integrates both topics. Part (a)–(b) thoroughly test D.2 (electric force, magnetic force, Wien selector balance). Parts (c)–(d) require circuit analysis from B.5 (voltage divider, internal resistance, leakage resistance in parallel with capacitor) to explain the experimental data and why transmission is incomplete. Neither topic is nominal; both are essential to the physics.

Iteration 1 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: (a) State [AO1] → (b)(i)–(c) Show/Determine [AO2] → (d) Explain [AO3]. Each tier uses appropriate command terms and builds in difficulty from recall through calculation to reasoned explanation with causal linkage.
command_structure fail

Part (d) violates §4.4.1 AO3 command-term structure for 'Explain'. M1 correctly exhibits an explicit causal chain ('spread of speeds THEREFORE only narrow band passes THEREFORE reduced fraction'), but M2 fails the requirement: it presents a listing of three alternative mechanisms without enforcing explicit 'X therefore Y' causal chains within each bullet. The mark scheme permits selecting 'any one of' three options (IR drop, ripple, fringing) but does not require each option's marking point to display the mandatory causal-chain structure. A student stating 'fringing fields exist' alone would satisfy the scheme without connecting it to deflection via explicit warrant.

FIX: Restructure M2 to enforce causal-chain marking points for each permitted mechanism. Example: 'M2 (IR-drop variant): The internal resistance r and series R cause an IR drop when leakage current fluctuates, **therefore** V_p (and E) drifts from the design value, **so** designed-speed ions experience residual deflecting force q(E − vB) and are lost. OR (fringing-field variant): Non-uniform electric field E at plate edges **therefore** ions entering near the edges experience off-axis force components, **so** some designed-speed ions are deflected and do not reach the exit. OR (ripple variant): Supply ripple/regulation causes E to oscillate about the nominal value, **therefore** ions passing through different phase of the oscillation experience different net forces, **so** transmission is reduced.' This ensures each permitted option explicitly links cause to consequence via physics warrant.
cross_theme pass

The question genuinely integrates both D.2 (Electric and magnetic fields) and B.5 (Current and circuits). Part (c) requires application of circuit theory (voltage divider with internal resistance and series resistance) to find the load resistance that produces the measured plate voltage—this is not mere name-checking. Part (d) explicitly demands explanation of transmission shortfall using both the Wien selector deflection physics (D.2: force balance on ions with speed spread) AND a circuit-related limitation (B.5: IR drop across internal/series resistance affecting plate voltage stability). Both topics are functionally necessary to answer the question fully.
discriminator pass

Part (d) explicitly asks students to 'Explain this shortfall' by reference to two distinct model limitations: (i) the spread in ion speeds entering the selector, and (ii) one circuit-related limitation of the supply. This requires critique of the idealized Wien selector model (infinite velocity resolution, perfect voltage stability) and its real-world constraints, with explicit causal links to the observed 78 % transmission. The mark scheme confirms M1 and M2 both demand linking language ('therefore,' 'so') connecting assumption failure to physical outcome.
rule_of_one fail

Part (b)(ii) is marked as 3 marks but has 3 award criteria (M1, M2, M3), which appears to match. However, M2 conflates two distinct operations: (1) calculating KE in joules using ½mv², and (2) converting joules to eV. These are logically separable steps that warrant distinct marking points. The mark scheme treats them as a single M2, leaving only 3 bullets for what should be 4 operations (formula selection, substitution, numerical answer in joules, conversion to eV). This violates the strict correspondence requirement for a Calculate/Determine part.

FIX: Expand part (b)(ii) to [4 marks] with M1: identifies KE = ½mv²; M2: substitutes values to get 3.01 × 10⁻¹⁴ J; M3: converts to eV (÷1.60 × 10⁻¹⁹) to obtain ~125 eV; M4: comment on consistency with table (peak at 125 eV). Alternatively, if part (b)(ii) must remain [3 marks], combine the formula and substitution into a single M1, then M2 = numerical answer in eV, M3 = consistency comment—but this sacrifices clarity of the calculation steps.
topic pass

The ERQ genuinely integrates both topics. D.2 (Electric and magnetic fields) is primary and dominates parts (a)–(b)–(d), covering force balance in the Wien selector, the v = E/B condition, and speed selection physics. B.5 (Current and circuits) is secondary but substantive in parts (c)–(d): part (c) requires a voltage-divider circuit analysis (Ohm's law, series resistors, EMF) to find the load resistance, and part (d) explicitly asks students to explain transmission loss via internal resistance effects on the supply voltage. Neither topic is superficial; both are conceptually essential to the scenario.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: (a) is AO1 State with justification; (b)(i)–(b)(ii) are AO2 Show that/Determine requiring calculation and data interpretation; (c)–(d) are AO3 Determine/Explain requiring analysis of trends and causal reasoning about circuit effects. Each tier builds appropriately on prior knowledge.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 'Explain' structure requirement. The primary M1 bullet lacks the mandatory explicit 'X therefore Y' causal chain: it states a fact (leakage current causes voltage drop) but does not explicitly link this to WHY the plate voltage differs from dial setting via a causal warrant. The structure 'A flows therefore V_p = ε − I(R+r)' is present, but the justification of the mechanism is incomplete—it should explicitly state 'leakage current I flows through (R + r) therefore voltage drop I(R + r) occurs therefore V_p < ε'. M2 correctly shows two causal links (lower V_p → lower E → lower balance speed → peak shifts), but M1 does not meet the minimum requirement of at least one fully explicit causal chain for 'Explain' commands.

FIX: Revise Part (d) M1 to: 'M1: A leakage current I flows continuously between the plates. This current passes through the series resistor R and internal resistance r, **therefore** a voltage drop I(R + r) develops across these resistors, **so** the voltage across the plates V_p = ε − I(R + r) is less than the emf ε [no ECF]'. This ensures two explicit causal steps ('current flows → voltage drop occurs → plate voltage reduced') matching the §4.4.1 Explain archetype. Alternatively, retain the leakage variant but ensure the mark scheme bullet explicitly states both logical steps as 'X therefore Y therefore Z' chain.
cross_theme fail

Part (d) is the only section nominally integrating both topics, but it functions as a circuit-analysis add-on that does not genuinely solve the physics problem using both D.2 and B.5 together. The Wien selector itself (parts a–c) is purely D.2; part (d) merely explains why the measured V_p differs from dial reading via circuit voltage division—B.5 appears only as a final justification, not as an integrated tool for solving the core selector physics. The two topics operate in sequence, not simultaneously.

FIX: Restructure the problem so that B.5 (circuit analysis) is essential to predicting or interpreting the selector's behaviour, not just appended as explanation. For example: (1) Ask students to derive the actual plate voltage V_p as a function of leakage current I and circuit parameters (R, r, ε), then use that V_p in the Wien balance equation to predict the selected speed—forcing simultaneous use of both topics; or (2) Frame part (d) as a 'determine' question asking students to calculate the leakage current I from the observed shift in peak voltage, using Ohm's law and the circuit loop equation alongside the Wien condition, making the circuit calculation integral to finding a physical quantity rather than merely explanatory.
discriminator fail

Part (d) is the final section and explicitly asks students to 'Explain... why the actual plate voltage may differ from the dial setting'. While this involves circuit reasoning, it does NOT ask the student to critique the model or discuss assumptions/limitations of the Wien selector model itself. The question assumes the selector works as designed and merely explains a practical circuit effect; it does not ask 'Discuss why the uniform-field assumption breaks down', 'Suggest why the measured peak differs from theory', or 'Critique the assumption that fringing effects are negligible'. This fails the model-critique dimension.

FIX: Restructure part (d) or add a new final part (e) that explicitly asks students to critique a core model assumption, e.g.: 'Discuss one assumption made in the Wien selector model and explain how violation of that assumption would affect the agreement between the calculated and observed ion speed' or 'The table shows a broadened peak rather than a sharp line. Suggest one physical reason why the model of ideal parallel plates with no fringing fields is insufficient to explain this broadening.' This would satisfy the dimension's requirement for model critique in the final part.
rule_of_one fail

Part (a) specifies 2 marks but lists only 2 award bullets (M1 and M2), yet each bullet describes a compound criterion (direction + justification) rather than distinct operations. The structure conflates "state direction" with "justify direction" into single marks, violating the 1-operation-per-mark principle. For a proper 2-mark "State" part, the scheme should separate: (i) state E and F are antiparallel, and (ii) justify why (net force = 0). Currently, M1 bundles both the antiparallel claim and its justification; M2 adds a second justification. This is ambiguous and does not cleanly map 2 marks to 2 distinct, sequenced operations.

FIX: Restructure part (a) mark scheme as: M1 — State that the electric force and magnetic force are antiparallel (opposite directions). M2 — Justify: for undeflected motion, net force must be zero; given fixed magnetic force qv×B, electric field E must be oriented so qE points opposite to qv×B (accept labelled diagram). This maps 2 marks cleanly to 2 distinct cognitive steps (state, then justify), each testable independently.
topic pass

The ERQ genuinely integrates both topics. Part (d) explicitly requires understanding of circuit elements (emf, internal resistance, series protection resistor, leakage current) from B.5 to explain why actual plate voltage differs from dial setting, while parts (a)–(c) test core D.2 concepts (velocity selector, electric and magnetic force balance, field strength). The causal chain in (d) directly links circuit behavior to field strength and ion selection, making both topics essential rather than superficial.

Planner output (stage 1)

Archetype: real-world device
Scenario: A particle accelerator uses crossed electric and magnetic fields to select particles of a specific velocity (velocity selector configuration). Particles enter horizontally with varying speeds; only those matching a design condition pass through undeflected. The accelerator circuit supplies the electric field via a high-voltage power supply, and the magnetic field is generated by permanent magnets. Students analyse the force balance, calculate the required field strengths, and evaluate how circuit voltage limitations and field non-uniformity affect the practical performance of the selector.
Cross-pollination part: d
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State
b(i)	3	AO2	Derive
b(ii)	3	AO3	Calculate
c	2	AO2	Determine
d	2	AO3	Explain

Generate another →