📚 AQA A-level Physics Unit 4 January 2019: Topic-by-Topic Revision | AQA A-level 物理 Unit 4 2019年1月：分主题复习
The January 2019 AQA Physics Unit 4 paper was a structured test of the second-year A-level topics: circular motion, simple harmonic motion, gravitational fields, electric fields, capacitance, magnetic fields and electromagnetic induction. To do well, you need to recall the key definitions, choose the correct equation, and present your working clearly.
2019年1月 AQA 物理 Unit 4 试卷系统考查了 A-level 第二学年的内容：圆周运动、简谐运动、引力场、电场、电容、磁场与电磁感应。要想考好，你需要准确回忆核心定义、选择正确公式，并清晰写出解题过程。
This article gives a topic-by-topic revision guide, with the equations you must remember and the exam strategies that earn marks. Use it alongside the official January 2019 question paper and mark scheme.
本文提供分主题复习指南，列出你必须记住的公式和能够得分的考试策略。建议配合官方 2019年1月真题和评分标准一起使用。
1. Understanding the Unit 4 Specification | 理解 Unit 4 考纲
Unit 4 is titled ‘Fields and Further Mechanics’. It builds on the AS topics but introduces more mathematical treatments, especially vectors, exponential decay and calculus-based ideas.
Unit 4 的官方名称为“场与进阶力学”。它以 AS 内容为基础，但引入了更多数学处理方法，尤其是矢量、指数衰减和微积分相关概念。
You should be familiar with the command words used in AQA questions, such as ‘show’, ‘prove’, ‘derive’, ‘state’, ‘calculate’ and ‘suggest’. Each word tells you how much working is expected.
你需要熟悉 AQA 题目中的指令词，如“证明”“推导”“写出”“计算”和“建议”。每个词都暗示了期望的作答深度。
In the paper, multiple-choice questions test quick recall and interpretation, while written questions require structured working. Always write the equation first, substitute numbers with units, and then evaluate.
试卷中，选择题考查快速回忆与理解，笔答题则要求结构化步骤。通常应先写出公式，再代入带单位的数值，最后计算。
2. Circular Motion | 圆周运动
Circular motion appears through the ideas of angular displacement, angular speed and centripetal acceleration. The radian is the natural unit for angle here.
圆周运动涉及角位移、角速度和向心加速度等概念。弧度是这里最自然的角度的单位。
The linear speed v is related to the angular speed ω by the radius r:
线速度 v 与角速度 ω 通过半径 r 相联系：
v = rω
For an object moving in a circle at constant speed, the direction of velocity changes continuously, so there is a centripetal acceleration directed towards the centre.
当物体以恒定速率做圆周运动时，速度方向持续改变，因此存在指向圆心的向心加速度。
a = v²/r = ω²r
The associated resultant force is found from Newton’s second law:
对应的合力由牛顿第二定律给出：
F = mv²/r = mω²r
Common past-paper situations include the horizontal circle, the vertical loop and the conical pendulum.
常见真题情景包括水平圆周运动、竖直圆环和圆锥摆。
At the top of a vertical loop, the forces on an object include weight and the track or string force. At the minimum speed for completing the loop, the reaction force becomes zero at the top, so the weight alone provides the centripetal force.
在竖直圆环顶部，物体受力包括重力和轨道或绳的拉力。若要求刚好通过最高点，则顶部支持力为零，完全由重力提供向心力。
3. Simple Harmonic Motion | 简谐运动
Simple harmonic motion occurs when acceleration is proportional to displacement from equilibrium and directed back towards the equilibrium position.
简谐运动发生在加速度与相对平衡位置的位移成正比，且方向始终指向平衡位置的时候。
a = −ω²x
Here x is displacement, A is amplitude and ω is angular frequency. The negative sign shows that acceleration opposes displacement.
式中 x 为位移，A 为振幅，ω 为角频率。负号表示加速度与位移方向相反。
Displacement and velocity are often written as:
位移与速度常写成：
x = A cos(ωt), v = ±ω√(A² − x²)
Maximum speed occurs at the equilibrium position, where x = 0:
最大速度出现在平衡位置，即 x = 0 处：
vmax = ωA
For a mass on a spring, the period is determined by the mass and spring constant:
对于弹簧振子，周期由质量和劲度系数决定：
T = 2π√(m/k)
For a simple pendulum, the period depends on the length of the string and gravitational field strength:
对于单摆，周期取决于摆长和重力场强度：
T = 2π√(l/g)
In the January 2019 series, students were expected to interpret graphs of displacement, velocity and acceleration against time. The acceleration graph is always an inverted version of the displacement graph for SHM.
在2019年1月考试中，考生需要会解读位移、速度和加速度随时间变化的图像。对于简谐运动，加速度图像始终是位移图像的颠倒形式。
4. Gravitational Fields | 引力场
Gravitational fields are radial around point masses. The force between two point masses follows Newton’s law of gravitation:
引力场在点质量周围呈球形分布。两个点质量之间的引力服从牛顿万有引力定律：
F = GMm/r²
Gravitational field strength is defined as force per unit mass:
引力场强度定义为单位质量所受引力：
g = GM/r²
Gravitational potential V at a point is the work done per unit mass to bring a small mass from infinity to that point:
引力势 V 表示将单位质量的小物体从无穷远处移动到该点所做的功：
V = −GM/r
The minus sign indicates that gravitational potential is zero at infinity and decreases as the mass approaches a body.
负号表示无穷远处引力势为零，随着物体靠近中心天体，引力势逐渐降低。
For circular orbits, the gravitational force provides the centripetal force:
在圆轨道中，万有引力提供向心力：
GMm/r² = mv²/r
This leads to the orbital speed equation v = √(GM/r).
由此可得轨道速率公式 v = √(GM/r)。
Past papers often ask you to show that the period T satisfies T² ∝ r³. Start from the orbital condition and substitute v = 2πr/T.
真题经常要求你证明 T² ∝ r³。解题时可以从轨道条件出发，代入 v = 2πr/T。
5. Electric Fields | 电场
Electric fields are also radial fields. Coulomb’s law gives the force between two point charges:
电场同样属于径向场。库仑定律给出了两个点电荷之间的力：
F = Q₁Q₂ / (4πε₀r²)
Electric field strength is defined as force per unit positive charge:
电场强度定义为单位正电荷所受的力：
E = F/Q
For a radial field around a point charge, the field strength is:
对于点电荷周围的径向电场，场强为：
E = Q / (4πε₀r²)
Between two parallel conducting plates, the field is uniform. The field strength is related to the potential difference across the plates:
在两块平行导体板之间，电场是匀强电场。场强与两极板间电势差的关系为：
E = V/d
Electric potential V at a distance r from a point charge can be written as:
距点电荷 r 处的电势可以写作：
V = Q / (4πε₀r)
Always distinguish between gravitational potential and electric potential: electric potential is scalar and can be positive or negative, while gravitational potential is always negative.
注意区分引力势与电势：电势是标量，可为正也可为负；而引力势始终为负。
6. Capacitance | 电容
A capacitor stores electric charge. Capacitance is defined as charge stored per unit potential difference:
电容器储存电荷。电容定义为储存电荷量与电势差之比：
C = Q/V
The energy stored in a capacitor can be written in three useful forms:
电容器储存的能量有三种常用表达式：
E = ½QV = ½CV² = ½Q²/C
For a parallel plate capacitor, capacitance depends on the geometry and the dielectric material:
平行板电容器的电容取决于极板面积、间距以及电介质材料：
C = ε₀εᵣA/d
Here A is the area of overlap, d is the plate separation, ε₀ is the permittivity of free space and εᵣ is the relative permittivity of the dielectric.
其中 A 为极板重叠面积，d 为极板间距，ε₀ 为真空介电常数，εᵣ 为电介质的相对介电常数。
When a capacitor discharges through a resistor, the charge decays exponentially:
当电容器通过电阻放电时，电荷按指数规律衰减：
Q = Q₀e^(−t/RC)
The product RC is called the time constant. After one time constant, the charge has fallen to 0.37Q₀, that is e⁻¹ of its initial value.
乘积 RC 称为时间常数。经过一个时间常数后，电荷降为初始值的 0.37Q₀，即 e⁻¹ 倍。
Exam questions often ask you to check the units of RC. Since R is in ohms and C is in farads, the product is in seconds.
真题常要求你检验 RC 的单位。R 的单位是欧姆，C 的单位是法拉，两者相乘后单位为秒。
7. Magnetic Fields | 磁场
Magnetic fields exert forces on moving charges and current-carrying conductors. The force on a straight wire of length l carrying current I in a magnetic field B is:
磁场对运动电荷和通电导体会产生力的作用。长度为 l、通有电流 I 的直导线在磁感应强度为 B 的磁场中所受的力为：
F = BIl sin θ
Here θ is the angle between the wire and the direction of the magnetic field. When θ = 90°, the force is maximum; when θ = 0°, the force is zero.
式中 θ 为导线与磁场方向之间的夹角。当 θ = 90° 时力最大；当 θ = 0° 时力为零。
A single charged particle moving with speed v perpendicular to a magnetic field experiences a force:
单个带电粒子以速度 v 垂直于磁场运动时受力为：
F = Bqv
This force acts at right angles to the velocity, so it changes the direction of motion but not its speed. As a result, a charged particle moves in a circular path.
该力始终垂直于速度方向，因此它改变运动方向但不改变速率。因此，带电粒子将做圆周运动。
Equating the magnetic force to the centripetal force gives the radius of the path:
将磁场力与向心力相等，可得轨道半径：
r = mv/Bq
A common mistake is to use the diameter of the circular path instead of the radius. Read the question carefully and sketch the path if needed.
常见错误是把圆轨迹的直径当作半径使用。要仔细审题，必要时画出运动路径示意图。
8. Electromagnetic Induction | 电磁感应
Magnetic flux Φ through a coil is defined as the product of the magnetic flux density and the area through which it passes:
磁通量 Φ 定义为磁感应强度与垂直穿过面积之积：
Φ = BA cos θ
Here θ is the angle between the normal to the coil and the magnetic field. If the field is perpendicular to the plane of the coil, then θ = 0° and Φ = BA.
式中 θ 为线圈法线与磁场方向的夹角。如果磁场垂直于线圈平面，则 θ = 0°，Φ = BA。
Faraday’s law states that the induced emf is equal to the negative rate of change of magnetic flux linkage:
法拉第定律指出，感应电动势等于磁通链变化率的负值：
ε = −N dΦ/dt
N is the number of turns on the coil. Increasing the number of turns increases the induced emf for the same change in flux.
N 为线圈匝数。在相同磁通变化下，增加匝数会增大感应电动势。
Lenz’s law explains the negative sign: the direction of the induced current is always such that it opposes the change producing it.
楞次定律解释了负号：感应电流的方向总是阻碍引起感应电流的磁通变化。
In past papers, you may be asked to justify the direction of the current using Lenz’s law. State clearly whether the magnetic flux is increasing or decreasing, then describe the direction of the induced magnetic field that opposes the change.
真题中常要求你用楞次定律说明感应电流方向。应先说明磁通量是增大还是减小，再描述感应磁场朝哪个方向阻碍这种变化。
9. Alternating Currents and Transformers | 交流电与变压器
An alternating current is one that reverses direction periodically. The standard equation for an alternating voltage is:
交变电流是方向周期性变化的电流。交变电压的标准表达式为：
V = V₀ sin(2πft)
Here V₀ is the peak voltage and f is the frequency. The root-mean-square value is used to compare alternating current with direct current.
其中 V₀ 为峰值电压，f 为频率。均方根值用于将交流与直流进行比较。
Vrms = V₀ / √2, Irms = I₀ / √2
The average power dissipated in a resistor is given by P = IrmsVrms = Vrms²/R.
电阻中的平均功率为 P = IrmsVrms = Vrms²/R。
A transformer changes the alternating voltage using two coils wound around a soft iron core. For an ideal transformer:
变压器通过绕在软铁芯上的两个线圈改变交变电压。对于理想变压器：
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