PART I · PAPER 1 STYLE第一部分 · 第一卷风格Short structured · calculator · 30 marks短结构题 · 可用计算器 · 30 分
Short Structured Items短结构题
Show all working in the space below each question. Marks are awarded for correct method as well as final answers. Always state the direction or nature (attraction or repulsion) separately from any magnitude. Give numerical answers to an appropriate number of significant figures.在每题下方空白处写出全部解题过程。方法分（method marks）与最终答案同等重要。方向或性质（吸引或排斥）须与大小分开说明。数值答案保留适当的有效数字。
Q1MEDIUMPaper 1Coulomb's law + inverse-square scaling库仑定律与平方反比缩放[4 marks]
Two small spheres carry charges $q_1 = +2.0\ \mathrm{nC}$ and $q_2 = +8.0\ \mathrm{nC}$ and are held $3.0\ \mathrm{cm}$ apart in vacuum.真空中两个小球带电 $q_1 = +2.0\ \mathrm{nC}$ 与 $q_2 = +8.0\ \mathrm{nC}$，相距 $3.0\ \mathrm{cm}$ 固定。
(a)Calculate the magnitude of the electrostatic force on $q_1$ and state whether it is attractive or repulsive.计算 $q_1$ 所受静电力的大小，并说明是吸引还是排斥。[2]
(b)The separation is now reduced to $1.5\ \mathrm{cm}$ with the charges unchanged. State, with a reason, the new magnitude of the force.在电荷不变的情况下，将间距减小到 $1.5\ \mathrm{cm}$。写出力的新大小并说明理由。[2]
Q2MEDIUMPaper 1magnetic field patterns + grip rule磁场图样与螺旋定则[4 marks]
A long straight horizontal wire carries a conventional current directed from west to east. A small plotting compass is placed directly above the wire.一根长直水平导线中常规电流由西向东。在导线正上方放一只小磁针（指南针）。
(a)State the shape of the magnetic field lines around the wire, and use the right-hand grip rule to determine the direction in which the magnetic field points at the point directly above the wire.写出导线周围磁感线的形状，并用右手螺旋定则判断导线正上方一点处磁场的方向。[2]
(b)The wire is now wound into a solenoid. State one feature of the magnetic field inside the solenoid, and explain why magnetic field lines always form closed loops.现将导线绕成螺线管。写出螺线管内部磁场的一个特征，并解释磁感线为何总是构成闭合回路。[2]
A point charge $Q = +5.0\ \mathrm{nC}$ is fixed in vacuum.真空中固定一点电荷 $Q = +5.0\ \mathrm{nC}$。
(a)Calculate the electric field strength at a distance $r = 0.10\ \mathrm{m}$ from $Q$, and state its direction.计算距 $Q$ 为 $r = 0.10\ \mathrm{m}$ 处的电场强度，并说明其方向。[2]
(b)A test charge $q = -3.0\ \mathrm{nC}$ is placed at that point. Calculate the magnitude of the force on it and state its direction relative to $Q$.在该点放置检验电荷 $q = -3.0\ \mathrm{nC}$。计算它所受力的大小，并说明其相对 $Q$ 的方向。[2]
(c)A second identical charge $+5.0\ \mathrm{nC}$ is now fixed a short distance away. State the value of the resultant electric field strength at the exact midpoint between the two charges, justifying your answer with a symmetry argument.现在在不远处再固定一个相同的电荷 $+5.0\ \mathrm{nC}$。写出两电荷正中点处合电场强度的值，并用对称性论证你的答案。[2]
Q4HARDPaper 1uniform field between plates平行板间的匀强场[6 marks]
Two horizontal parallel plates are separated by $d = 5.0\ \mathrm{cm}$ and connected to a $V = 250\ \mathrm{V}$ supply. An electron (charge magnitude $e$, mass $m_e = 9.11\times 10^{-31}\ \mathrm{kg}$) is released between them.两水平平行板相距 $d = 5.0\ \mathrm{cm}$，接 $V = 250\ \mathrm{V}$ 电源。一个电子（电荷大小为 $e$、质量 $m_e = 9.11\times 10^{-31}\ \mathrm{kg}$）在板间释放。
(a)Calculate the electric field strength between the plates and state two features of the field-line pattern.计算板间的电场强度，并写出电场线图样的两个特征。[2]
(b)Calculate the magnitude of the electric force on the electron.计算电子所受电力的大小。[2]
(c)Hence calculate the magnitude of the electron's acceleration, and state why this value is the same everywhere between the plates.由此计算电子加速度的大小，并说明为何该值在板间各处相同。[2]
A point charge $Q = +6.0\ \mathrm{nC}$ is fixed in vacuum. Point $A$ is at $r_A = 0.20\ \mathrm{m}$ from $Q$ and point $B$ is at $r_B = 0.60\ \mathrm{m}$ from $Q$.真空中固定一点电荷 $Q = +6.0\ \mathrm{nC}$。点 $A$ 距 $Q$ 为 $r_A = 0.20\ \mathrm{m}$，点 $B$ 距 $Q$ 为 $r_B = 0.60\ \mathrm{m}$。
(a)Calculate the electric potential at $A$ and at $B$.计算 $A$ 与 $B$ 处的电势。[2]
(b)An external agent moves a charge $q = +4.0\ \mathrm{nC}$ from $B$ to $A$. Calculate the work done by the agent.外力把电荷 $q = +4.0\ \mathrm{nC}$ 从 $B$ 移到 $A$。计算外力所做的功。[2]
(c)State the sign of the work done and explain it in terms of the potential energy of the charge. State also the work done in moving $q$ along an equipotential surface.写出所做功的正负号，并结合电荷的电势能加以解释。同时写出把 $q$ 沿等势面移动所做的功。[2]
Q6MEDIUMPaper 1comparing gravitational, electric, magnetic fields引力场、电场、磁场对比[4 marks]
A student compares the gravitational field of a point mass with the electric field of a point charge, and then with the magnetic field of a bar magnet.一名学生将点质量的引力场与点电荷的电场对比，再与条形磁铁的磁场对比。
(a)State one similarity in the force laws for the gravitational and electric fields, and one fundamental difference in the nature of the forces.写出引力场与电场的力定律的一个相似点，以及力的性质上的一个根本区别。[2]
(b)Identify one way in which the field-line pattern of a magnetic field differs from that of an electric field, and link it to the absence of magnetic monopoles.指出磁场的场线图样与电场的一处不同，并将其与磁单极子不存在联系起来。[2]
PART II · PAPER 1B / DATA ANALYSIS第二部分 · 第一卷 B / 数据分析Graphs · data · uncertainties · 20 marks图像 · 数据 · 不确定度 · 20 分
Graph and Data Questions图像与数据题
These items reward correct linearisation, careful reading of gradients, and correct handling of uncertainties. Quote uncertainties to one significant figure and round the value to match.这些题考查正确的线性化、对斜率的细致读取以及对不确定度的正确处理。不确定度保留 1 位有效数字，并使数值的末位与之对齐。
A student measures the electric field strength $E$ at several distances $r$ from a small charged sphere in vacuum and tabulates $E$ against $1/r^2$:学生在真空中测量距一个带电小球若干距离 $r$ 处的电场强度 $E$，并将 $E$ 对 $1/r^2$ 列表：
$1/r^2\ /\ \mathrm{m^{-2}}$
$25$
$50$
$75$
$100$
$E\ /\ \mathrm{N\,C^{-1}}$
$90$
$180$
$270$
$360$
(a)Starting from the field equation for a point charge, show that a graph of $E$ against $1/r^2$ should be a straight line through the origin, and state what the gradient represents.从点电荷的场强公式出发，证明 $E$ 对 $1/r^2$ 的图应为过原点的直线，并说明斜率代表什么。[3]
(b)Calculate the gradient of the line, and hence determine the charge $Q$ on the sphere.计算该直线的斜率，由此求小球上的电荷 $Q$。[3]
(c)The value of $E$ at $1/r^2 = 100\ \mathrm{m^{-2}}$ has an absolute uncertainty of $\pm 10\ \mathrm{N\,C^{-1}}$. Calculate the percentage uncertainty in $E$ at this point.$1/r^2 = 100\ \mathrm{m^{-2}}$ 处的 $E$ 值绝对不确定度为 $\pm 10\ \mathrm{N\,C^{-1}}$。计算该点 $E$ 的百分比不确定度。[2]
(d)State one reason why plotting $E$ against $1/r^2$ is preferable to plotting $E$ against $r$ when finding $Q$.说明在求 $Q$ 时，作 $E$ 对 $1/r^2$ 的图相比作 $E$ 对 $r$ 的图更可取的一个原因。[2]
A student measures the electric potential $V_e$ at several distances $r$ from a charged sphere in vacuum and tabulates $V_e$ against $1/r$:学生在真空中测量距一个带电球若干距离 $r$ 处的电势 $V_e$，并将 $V_e$ 对 $1/r$ 列表：
$1/r\ /\ \mathrm{m^{-1}}$
$4.0$
$6.0$
$8.0$
$10.0$
$V_e\ /\ \mathrm{V}$
$36$
$54$
$72$
$90$
(a)Starting from the potential equation for a point charge, show that a graph of $V_e$ against $1/r$ should be a straight line through the origin, and state what the gradient represents.从点电荷的电势公式出发，证明 $V_e$ 对 $1/r$ 的图应为过原点的直线，并说明斜率代表什么。[3]
(b)Calculate the gradient of the line, and hence determine the charge $Q$ on the sphere.计算该直线的斜率，由此求球上的电荷 $Q$。[3]
(c)Using the data, calculate the work done by an external agent in moving a charge $q = +2.0\ \mathrm{nC}$ from the point where $1/r = 4.0\ \mathrm{m^{-1}}$ to the point where $1/r = 10.0\ \mathrm{m^{-1}}$.利用数据，计算外力把电荷 $q = +2.0\ \mathrm{nC}$ 从 $1/r = 4.0\ \mathrm{m^{-1}}$ 处移到 $1/r = 10.0\ \mathrm{m^{-1}}$ 处所做的功。[2]
(d)On a sketch of the radial field around the sphere, state how the equipotential surfaces are arranged relative to the field lines, and what their spacing indicates about the field strength.在球周围径向场的示意图上，说明等势面相对电场线如何排布，以及它们的疏密反映场强的什么信息。[2]
PART III · PAPER 2 STYLE第三部分 · 第二卷风格Extended structured · calculator · 30 marks长结构题 · 可用计算器 · 30 分
Extended Structured Problems长结构问题
Set up each problem with a clear diagram and labelled directions. Method marks dominate the longer items; carry intermediate values to extra figures and round only the final answer.每题先画清晰的示意图并标注方向。长题中方法分占比最大；中间值多保留几位，仅在最终答案处取舍有效数字。
Q9HARDPaper 2charged drop between parallel plates平行板间的带电液滴[12 marks]
Two horizontal parallel plates are separated by $d = 4.0\ \mathrm{cm}$. A charged oil droplet of mass $m = 4.0\times 10^{-15}\ \mathrm{kg}$ carries a charge $q = +8.0\times 10^{-19}\ \mathrm{C}$ and floats motionless between the plates when a potential difference $V$ is applied, with the upper plate positive.两水平平行板相距 $d = 4.0\ \mathrm{cm}$。一颗质量 $m = 4.0\times 10^{-15}\ \mathrm{kg}$、带电 $q = +8.0\times 10^{-19}\ \mathrm{C}$ 的带电油滴，在施加电势差 $V$（上板为正）时静止悬浮于板间。
(a)State the number of excess or missing electrons on the droplet, and explain how you decided whether they are excess or missing.写出油滴上多余或缺失的电子数，并说明你如何判断是多余还是缺失。[2]
(b)By balancing the forces on the droplet, calculate the electric field strength between the plates.通过对油滴受力平衡，计算板间的电场强度。[3]
(c)Hence calculate the potential difference $V$ applied across the plates.由此计算加在两板间的电势差 $V$。[3]
(d)The droplet now suddenly gains one further electron of the same sign while $V$ is unchanged. Determine the magnitude and direction of its initial acceleration. Comment on whether the suvat equations could describe the subsequent motion.在 $V$ 不变的情况下，油滴突然再获得一个同号电子。求其初始加速度的大小与方向，并评述 suvat 方程能否描述其后续运动。[4]
Two point charges $q_1 = +3.0\ \mathrm{nC}$ and $q_2 = +5.0\ \mathrm{nC}$ are fixed in vacuum a distance $r = 6.0\ \mathrm{cm}$ apart.真空中固定两点电荷 $q_1 = +3.0\ \mathrm{nC}$ 与 $q_2 = +5.0\ \mathrm{nC}$，相距 $r = 6.0\ \mathrm{cm}$。
(a)Calculate the electric potential energy of this pair of charges, and state whether external work was required to assemble the configuration from infinite separation.计算这对电荷的电势能，并说明从无穷远处组装该构型是否需要外力做功。[3]
(b)Calculate the resultant electric potential at the midpoint of the line joining the two charges.计算两电荷连线中点处的合电势。[3]
(c)State the work done by the electric field in moving a test charge around any closed path that returns to its starting point, and justify your answer using the idea of potential.写出电场在把检验电荷沿任意闭合路径移回起点时所做的功，并用电势的概念加以论证。[2]
(d)The separation between the two charges is now doubled. State, with a reason, the new electric potential energy of the pair.现在将两电荷的间距加倍。写出这对电荷的新电势能并说明理由。[2]
Q11HARDPaper 2magnetic patterns + field synthesis磁场图样与三场综合[8 marks]
An electromagnet is made by winding a coil of wire around a soft-iron core to form a solenoid. A bar magnet of the same overall shape is placed nearby for comparison.把导线绕在软铁芯上构成螺线管，从而制成电磁铁。在旁边放置一块整体形状相同的条形磁铁以作对比。
(a)Describe the magnetic field pattern around a bar magnet, stating the direction of the field lines outside the magnet and where the field is strongest.描述条形磁铁周围的磁场图样，写出磁铁外部磁感线的方向以及磁场最强之处。[2]
(b)Using the right-hand grip rule applied to the coils, explain how the positions of the north and south poles of the solenoid are determined, and state what happens to them if the current is reversed.对线圈运用右手螺旋定则，解释如何确定螺线管 N、S 极的位置，并说明电流反向时它们会如何变化。[2]
(c)Explain why the external field pattern of the solenoid is the same as that of the bar magnet, referring to the field lines inside and outside the coil.解释为何螺线管的外部场图样与条形磁铁相同，须涉及线圈内部与外部的磁感线。[2]
(d)Compare the magnetic field with the electric field of a point charge, identifying one similarity and one difference in their field-line patterns.将磁场与点电荷的电场对比，指出它们场线图样的一个相似点和一个不同点。[2]