📚 AS Physics: Unit 4 June 2019 Mark Scheme Experimental Investigation | 物理：2019年6月单元4评分标准实验探究
The June 2019 Edexcel International AS Physics Unit 4 paper (WPH14/01) included a core practical investigation that challenged students to determine the magnetic flux density of a uniform magnetic field by measuring the force on a current-carrying conductor. This article unpacks the experimental techniques, data handling, and common mistakes highlighted in the exam’s mark scheme. The analysis is based on the classic experiment where a rigid copper wire is placed between the poles of a permanent magnet and connected to a circuit, while an electronic balance measures the reaction force on the magnet.
2019年6月Edexcel国际AS物理第四单元（WPH14/01）试卷中有一道核心实验探究题，要求学生通过测量通电导线所受安培力来确定匀强磁场的磁通量密度。本文深入解析试卷评分标准中强调的实验操作、数据处理以及考生常见错误。分析基于经典实验——将一根硬质铜导线置于永久磁铁的两极之间并接通电路，同时用电子天平测量磁铁受到的反作用力。
1. Experimental Scenario and Objectives | 实验情境与目标
The exam question presented a set-up where a straight wire of measured length L is positioned horizontally inside a magnetic field produced by a pair of slab magnets placed on an electronic balance. When a current I flows through the wire, the magnetic force acts vertically. By Newton’s third law, the magnet experiences an equal and opposite vertical force, causing a change in the balance reading. The primary objective was to investigate the relationship between the magnetic force F and the current I, and hence determine the magnetic flux density B of the field within the magnet gap.
题目给出的装置是将一根已测量长度 L 的直导线水平放置在一对扁平磁铁产生的磁场中，磁铁置于电子天平上。当导线通有电流 I 时，磁场力沿竖直方向作用。根据牛顿第三定律，磁铁会受到等大反向的竖直力，从而使天平读数发生变化。实验主要目的是探究磁力 F 与电流 I 之间的关系，并由此确定磁极间隙内磁场的磁通量密度 B。
onal field strength g (9.81 m s⁻²), gives the magnetic force: F = Δm × g. By plotting an F– equals B × L, allowing B to be calculated if the conductor length L in the field is known.
评分标准对能够识记下列关系的考生给予加分：天平上测得的质量变化 Δm 乘以重力场强度 g（9.81 m s⁻²）即为磁力 F = Δm × g。通过绘制 F–I 图像，其斜率等于 B × L，在已知导线处于磁场中的长度 L 的条件下，即可计算出 B 值。
2. Apparatus and Circuit Arrangement | 仪器与电路安排
The essential apparatus listed in the mark scheme included: two slab-shaped neodymium or ceramic magnets placed on a sensitive electronic balance (resolution at least 0.01 g), a rigid copper or aluminium rod of known effective length, a variable DC power supply, an ammeter, a rheostat to smoothly vary current, connecting leads, and a ruler or vernier calliper to measure the length of wire inside the magnetic gap. A spirit level was often recommended to ensure the wire was truly horizontal so that the force direction was purely vertical.
评分标准列出的关键仪器包括：两块扁平钕磁铁或陶瓷磁铁，放置在分辨率至少为 0.01 g 的灵敏电子天平上；一根已知有效长度的硬质铜棒或铝棒；可变直流电源；电流表；用于平滑调节电流的变阻器；连接导线；以及测量导线在磁隙内长度的直尺或游标卡尺。通常还建议使用水准仪确保导线严格水平，使受力方向纯竖直。
An important marking point was the correct orientation of the magnets. The magnetic field must be horizontal and perpendicular to the wire. The diagram commonly showed a yoke configuration, with the wire passing between the N and S poles. The balance should be zeroed when the magnets are in position but before the current is switched on. The ammeter was placed in series with the wire, and the rheostat was used to set a range of currents from small values up to approximately 5 A, with close monitoring to avoid overheating.
评分标准中的一个重要得分点是磁铁的摆放方向必须正确：磁场应呈水平方向且与导线垂直。常见示意图为磁轭式结构，导线穿过 N 极与 S 极之间。天平应在磁铁就位但尚未接通电流时调零。电流表与导线串联，变阻器用于设定从小电流到约 5 A 之间的多个电流值，并密切监测以防过热。
3. Underlying Physics and Equations | 基本物理原理与方程
s the angle between the current direction and the magnetic field. In this experiment θ = 90°, so sin θ = 1, simplifying the relationship to F = B I L. The mark scheme accepted the direct proportionality F ∝ d and the current is not so high as to generate significant heating and resistance change.
在磁通量密度为 B 的匀强磁场中，长度为 L 的通电直导线所受磁力为 F = B I L sin θ，其中 θ 是电流方向与磁场方向之间的夹角。本实验中 θ = 90°，故 sin θ = 1，关系简化为 F = B I L。评分标准接受正比关系 F ∝ I，前提是导线完全处于匀强磁场中且电流不过大，避免产生明显的发热和电阻变化。
Candidates were expected to derive the gradient of the F– re B = gradient / L. The mark scheme insisted on stating the correct units: F in newtons, I in amperes, gradient in N A⁻¹, L in metres, giving B in teslas (T).
考生应能推导 F–I 图像的斜率。由 F = B I L 可知，以 F 为纵轴、I 为横轴作图，将得到一条过原点的直线，斜率 = B L。因此 B = 斜率 / L。评分标准强调必须注明正确单位：F 为牛顿，I 为安培，斜率单位为 N A⁻¹，L 为米，最终 B 的单位为特斯拉（T）。
4. Key Mark Scheme Requirements for Data Collection | 数据收集的评分要点
The mark scheme allocated marks for recording a table of at least six different current values and the corresponding balance reading (mass). Each current was to be set by adjusting the rheostat, and the balance reading was noted after allowing the system to stabilise. For each current, the mass with the current on and the mass with the current off were taken, and the difference Δm was calculated. This method accounted for any drift in the balance zero or magnetic hysteresis.
评分标准中对记录至少六组不同电流值及对应天平读数（质量）的数据表设定了得分点。每次通过调节变阻器设定电流，待系统稳定后记录天平示数。对每个电流值，分别记录通电时与断电时的质量，并计算差值 Δm。这种方法可消除天平零点漂移或磁滞的影响。
ata were to be given to the appropriate precision as determined by the instrument, usually to the nearest 0.01 g for the balance and 0.1 A for the ammeter. Repeated readings were not always required but could be rewarded under 'technique' f the candidate described taking repeat measurements and averaging to reduce random error.
考官还关注力 F = Δm × g 的计算，g 取 9.81 m s⁻²。若明确注明，允许使用 g = 9.8 m s⁻²。所有原始数据须符合仪器决定的合适精度，通常天平精至 0.01 g，电流表精至 0.1 A。虽不强制要求重复测量，但若考生描述进行重复测量并取平均值以减小随机误差，则可在“实验技术”项获得奖励。
5. Graph Plotting and Gradient Determination | 绘图与斜率测定
The mark scheme stressed that the F– t-fit straight line drawn. Candidates who simply joined the dots lost marks. The line should go through the origin within experimental uncertainty – he two chosen points clearly stated and substituted into gradient = (F₂ − F₁) / (I₂ − I₁).
评分标准强调，F–I 图须在坐标纸上绘制且选用合理的分度值，占据图纸一半以上面积。各数据点应准确描画，并作一条最佳拟合直线。只是简单连点成线的考生会被扣分。该直线应在实验不确定度范围内通过原点——这是对正比关系的明确检验。计算斜率须使用一个较大的直角三角形，清晰标注所选两点的坐标，并代入公式：斜率 = (F₂ − F₁) / (I₂ − I₁)。
The uncertainty in the gradient was often assessed. The mark scheme expected candidates to draw either worst-fit lines (e.g., maximum and minimum gradient lines) or to state that the percentage uncertainty in the gradient equals the percentage uncertainty in F plus the percentage uncertainty in I, though for Unit 4 the graphical method was preferred. The final value of B was then stated as gradient / L with its absolute uncertainty.
通常还要评估斜率的不确定度。评分标准期望考生要么绘制最差拟合线（例如最大和最小斜率线），要么说明斜率的百分不确定度等于 F 的百分不确定度与 I 的百分不确定度之和，但在第四单元中图形法更为可取。最终 B 值以 斜率 / L 的形式给出，并附上其绝对不确定度。
6. Determining the Effective Length L of the Conductor | 导线有效长度 L 的测定
A frequent source of error was the incorrect measurement of L. The effective length is the length of the wire that is actually inside the uniform magnetic field region. The mark scheme required using a ruler or digital callipers to measure the width of the magnet poles across the gap. However, when slab magnets are used with a steel yoke, the field may only be uniform within a central region. Candidates were expected to measure the distance between the inner edges of the pole pieces where the wire enters and exits the field.
一个常见的误差来源是 L 的测量不当。有效长度指引线实际处于匀强磁场区域内的长度。评分标准要求使用直尺或数显游标卡尺测量磁极间隙的宽度。然而，当使用带钢轭的扁平磁铁时，磁场可能仅在中心区域均匀。考生应测量导线进出磁场处的磁极内侧间距。
sing a vernier calliper. The percentage uncertainty in L contributed directly to the final uncertainty in B. A well-structured answer typically included a statement like: "L = (4.0 ± 0.1) cm, giving a percentage uncertainty of 2.5%."
评分标准对在磁隙不同位置对 L 进行多次测量并取平均的做法给予加分。读数用游标卡尺精确记录至 0.1 mm。L 的百分不确定度会直接传递到 B 的最终不确定度中。一份结构严谨的答案通常会包含这样的表述：“L = (4.0 ± 0.1) cm，百分不确定度为 2.5%。”
7. Sources of Uncertainty and Their Minimisation | 不确定度来源及减小方法
ich when multiplied by g produced an uncertainty in force. The ammeter resolution yielded ±0.05 A or similar. Fluctuations in the balance reading due to air currents or vibrations were a source of random error. Candidates were credited for suggesting the use of a draft shield or placing the balance on a vibration-free bench.
评分标准指出了几个主要不确定度来源。电子天平的分辨力（±0.01 g）带来质量的不确定度，乘以 g 后转换为力的不确定度。电流表的分辨力产生的典型值为 ±0.05 A 等。气流或振动引起的天平读数波动是随机误差的来源。考生若能建议使用防风罩或将天平置于防震台上，即可获得加分。
Systematic errors included zero error on the balance, inaccurate g value, or the magnetic field not being perfectly perpendicular to the wire. To minimise systematic error, the balance was to be re-zeroed before each set of readings, and the spirit level was used to align the wire. The mark scheme also noted that reversing the current and averaging the magnitudes of the force could cancel out any small misalignment effects or the influence of the Earth’s magnetic field.
系统误差包括天平零点误差、所用 g 值不准确，或磁场不完全垂直于导线。为减小系统误差，每轮读数前应重新调零天平，并用水准仪校准导线水平。评分标准还指出，通过调换电流方向并对力的大小取平均，可以抵消任何微小的不对中影响或地磁场的影响。
8. Common Student Errors Highlighted in the Mark Scheme | 评分标准中指出的考生常见错误
A very common mistake was forgetting to subtract the zero-current mass reading. Students often recorded the balance reading with current on but did not take the corresponding off-current reading, leading to a false force calculation. The mark scheme explicitly required the difference Δm. Another frequent error was using incorrect units, for instance plotting mass (in grams) instead of force (in newtons), which produced a gradient that was out by a factor of g.
一个十分常见的错误是忘记减去零电流时的质量读数。学生常常只记录通电时的天平示数，而未记录对应断电时的读数，导致力的计算错误。评分标准明确要求计算差值 Δm。另一常见错误是使用了错误的单位，例如直接用质量（克）而非力（牛顿）作图，这样得到的斜率会因差一个 g 因子而出错。
0. The mark scheme allowed a small intercept due to experimental uncertainty, but the line should be judged on its overall fit. Also, some students used the formula F = BIL directly to calculate B for each pair of values and then averaged them. While mathematically valid, this approach did not meet the graphical analysis requirements and often missed marks for gradient determination and uncertainty evaluation.
许多考生因所绘的最佳拟合线未通过原点而失分，尽管物理规律要求当 I = 0 时 F 必为 0。评分标准允许因实验不确定度而存在微小截距，但必须基于整体拟合程度进行评判。此外，部分学生直接用公式 F = BIL 逐对计算 B 再取平均值。尽管数学上可行，但这种方法不符合图像分析要求，通常得不到斜率测定和不确定度评定方面的分数。
9. Safety Precautions and Practical Technique | 安全注意事项与实验操作技巧
The mark scheme reserved marks for sensible safety measures. The main risks were overheating of the wire at high currents, potentially causing burns or melting insulation, and the strong magnetic field affecting electronic devices. Candidates were expected to switch off the current between readings, use a heat-resistant mat, and avoid touching the wire. If neodymium magnets were used, a warning about pinching hazards and pacemaker interference was sometimes credited.
评分标准为合理的安全措施设有专项得分。主要风险包括大电流下导线过热，可能造成灼伤或熔化绝缘层，以及强磁场对电子设备的影响。考生应提及在读数间隙断开电流、使用耐热垫，以及避免触碰导线。若使用钕磁铁，对夹伤风险和心脏起搏器干扰的警告有时也会给分。
On the technique side, the mark scheme commended ensuring the wire was rigid and straight, with no sagging, which would alter the effective length and angle. Clamping the wire firmly at both ends with crocodile clips and positioning the magnet centrally under the wire improved repeatability. Additionally, allowing a few seconds for the balance to settle after changing the current reduced random fluctuations. The current should never exceed the ammeter’s range and was typically kept below 5 A to avoid heating effects that could change the wire’s resistance and thus the current itself.
在操作技巧方面，评分标准赞赏确保导线刚硬、笔直、无下垂，避免改变有效长度和角度。将导线两端用鳄鱼夹牢固夹紧，并将磁铁置于导线正下方中心位置，可提高重复性。此外，每次改变电流后让天平静置数秒以减少随机波动。电流绝不可超过电流表量程，通常维持在 5 A 以下以免发热导致导线电阻变化，进而影响电流本身。
10. Applying the Mark Scheme to Improve Exam Performance | 运用评分标准提升应试表现
To score full marks on this type of experimental question, students must present their work in a logical sequence: statement of variables, labelled diagram, table with correct headings and units, force calculation, graph with best-fit line, gradient calculation with working, final B value with uncertainty, and a brief evaluation. The June 2019 mark scheme particularly rewarded clear communication of the proportional relationship and the justification that the line through the origin validates F ∝ I.
要在此类实验题中获得满分，学生必须按逻辑顺序呈现作答：变量说明、带标注的示意图、表头正确且含有单位的表格、力的计算、带最佳拟合线的图像、附有计算过程的斜率求算、包含不确定度的最终 B 值，以及简要评估。2019 年 6 月的评分标准特别嘉奖对正比关系的清晰表述，以及对通过原点的直线验证了 F ∝ I 的合理解释。
Mark schemes also highlight the importance of using the correct number of significant figures. Typically, the final value of B should be quoted to two or three significant figures, consistent with the least precise measurement. When stating the uncertainty, many candidates lost a mark by giving an absolute uncertainty with more decimals than the measurement itself. The best responses coupled the result with a percentage difference from an accepted value (e.g., 0.065 T) and identified the main contributor to the total uncertainty, usually the measurement of L or the balance resolution.
评分标准还强调使用正确有效数字位数的重要性。通常最终 B 值应保留两到三位有效数字，与最不精确的测量保持一致。在表述不确定度时，许多考生因给出的绝对不确定度的小数位数多于测量值而失分。最佳答卷会将实验结果与公认值（如 0.065 T）比较，计算百分差，并明确指出总不确定度的主要贡献项——通常是 L 的测量或天平分辨力。
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