📚 IB WJEC Physics: Tricky Questions Explained | IB WJEC 物理：易错题精讲
Many high-achieving physics students lose marks not because they lack understanding, but because they fall into carefully designed traps. This article targets the most common pitfalls in IB and WJEC physics, offering clear, focused explanations that turn confusion into confidence. By studying each tricky concept side‑by‑side in English and Chinese, you will sharpen your ability to spot errors before they catch you in an exam.
很多物理成绩不错的学生丢分，并非因为知识欠缺，而是掉进了考题精心设计的陷阱。本文针对 IB 和 WJEC 物理中最常见的易错点，提供清晰、聚焦的解析，帮你把困惑变成把握。通过中英文对照学习每一个易错概念，你将练就一双火眼金睛，在考试中提前识别出那些容易出错的细节。
1. Newton’s Third Law vs Equilibrium | 牛顿第三定律与平衡力混淆
Students often think that when a book rests on a table, the downward weight and the upward normal force are an action–reaction pair. This is incorrect. Newton’s third law forces must act on two different objects. The weight is the Earth pulling the book; its third‑law partner is the book pulling the Earth upwards. The normal force is the table pushing the book; its partner is the book pushing down on the table. The equality of weight and normal force here arises from equilibrium (ΣF=0), not from the third law.
学生常常误以为，当一本书静置于桌面上时，向下的重力和向上的支持力是一对作用力与反作用力。这是错误的。牛顿第三定律要求两个力必须作用在不同的物体上。重力是地球对书的吸引，其反作用力是书对地球向上的吸引力。支持力是桌面对书的推力，其反作用力是书对桌面向下的压力。此时重力与支持力相等，是由于书处于平衡状态（合力为零），并非第三定律的直接结果。
A classic exam trap: a rocket pushes exhaust gases backward; the gases push the rocket forward. Some candidates claim these two forces cancel, so the rocket should move at constant speed. But the forces act on different objects (rocket and gases) and therefore cannot cancel on the rocket. The rocket accelerates because the net force on the rocket is the forward thrust.
经典的考试陷阱：火箭向后推燃气，燃气向前推火箭。有考生说这两个力抵消，所以火箭应该匀速运动。实际上，这两个力作用在不同物体（火箭和燃气）上，因此对火箭而言根本无法抵消。火箭之所以加速，是因为作用在火箭上的合力就是向前的推力。
2. Electric Potential vs Electric Potential Energy | 电势与电势能的区分
Electric potential V at a point is the potential energy per unit positive charge. A common mistake is to assume that a positive charge always moves from high potential to low potential spontaneously, or that a point with high potential always has high potential energy. The potential energy U of a charge q at a point is U = qV. For a negative charge, even if V is large and positive, U is large and negative, so it spontaneously moves towards higher potentials.
电势 V 指的是单位正电荷在某点的电势能。常见错误是认为正电荷总是自发地从高电势向低电势运动，或者高电势处电势能就一定大。实际上，电势能 U = qV。对于负电荷而言，即使 V 为正且很大，U 却是很大的负值，所以负电荷会自发向电势升高的方向运动。
In uniform electric fields, many students mix up the sign of work done by the field. When an electron moves against the field direction (towards the positive plate), the electric field does negative work on it, but its potential energy decreases if it moves to a lower potential? Check: electron moving towards positive plate is moving to higher potential, its U = (-e)V becomes more negative, so potential energy decreases — consistent with kinetic energy increase. Always track the charge sign.
在匀强电场中，很多学生对电场力做功的正负含糊不清。当一个电子逆着电场方向（向正极板）运动时，电场力做负功，但它的电势能是增大还是减小？要小心：电子向正极板运动是向高电势运动，U = (-e)V 变得更负，所以电势能减小——这与动能增大一致。务必始终关注电荷的符号。
3. Phase Difference and Path Difference | 相位差与波程差
In wave superposition questions, students frequently confuse phase difference (in radians or degrees) with path difference (in metres). The relationship is Δφ = (2π/λ) × Δx. A path difference of exactly one wavelength λ gives a phase difference of 2π rad, not zero. Many will incorrectly say that waves that have travelled the same distance are always in phase — they must have started in phase as well.
在波的叠加题目中，学生经常混淆相位差（弧度或度）与波程差（米）。它们的关系是 Δφ = (2π/λ) × Δx。一个波长的波程差对应 2π 弧度的相位差，而不是零。很多人错误地认为只要两列波传播的距离相等就一定是同相——实际上，还必须它们初始时刻就是同相的。
Exam favourite: two coherent sources in phase. A point where the path difference is 2.5λ is a point of destructive interference because the phase difference is 5π rad, an odd multiple of π. Always express the condition for minima as Δx = (m + ½)λ and for maxima as Δx = mλ, but only if the sources are in phase. If sources are out of phase, the conditions swap.
考试热门：两个同相相干波源，某点的波程差为 2.5λ，该点是相消干涉，因为相位差为 5π 弧度，是 π 的奇数倍。记住，只有当波源同相时，极小条件才是 Δx = (m + ½)λ，极大条件为 Δx = mλ。若波源反相，条件恰好互换。
4. Misunderstanding Terminal Velocity | 对终极速度的误解
When an object falls through a fluid and reaches terminal velocity, many students believe the net force is zero because air resistance vanishes. The truth is that resistive forces increase with speed, so at terminal velocity the upward drag plus upthrust exactly balance the weight, resulting in zero acceleration. The object does not stop experiencing air resistance; the resistance just stops increasing.
物体在流体中下落并达到终极速度时，许多学生认为合力为零是因为空气阻力消失了。事实上，阻力随速度增大而增大，达到终极速度时，向上的阻力和浮力之和与重力恰好平衡，加速度为零。物体并非不再受阻力作用，只是阻力不再增大而已。
Another slip: thinking terminal velocity is the same for all objects of the same mass. A spread‑eagle skydiver has a much lower terminal speed than a head‑down diver because of larger cross‑sectional area and shape. Be comfortable using the drag equation D ∝ v² or D ∝ v depending on the context, and interpreting velocity–time graphs with decreasing gradient.
另一个疏漏：以为相同质量的物体终极速度都一样。四肢张开的跳伞者终极速度远小于头朝下的落体，因为迎风面积和形状不同。要熟练运用阻力公式 D ∝ v² 或 D ∝ v（视情境而定），并能解读斜率逐渐减小的速度–时间图线。
5. Internal Resistance and Lost Volts | 内阻与内电压
When a battery delivers current, its terminal potential difference is lower than its emf because of the internal resistance r. The lost voltage is Ir. Students mistakenly treat emf ε as constant terminal voltage regardless of current. The correct terminal voltage is V = ε − Ir. In a circuit, if the external resistance decreases, current increases, lost volts increase, and V drops — this is why a heavily loaded battery appears ‘flat’.
当电池输出电流时，由于其内阻 r，路端电压会低于电动势。损失的电压为 Ir。学生常误以为电动势 ε 就是不管电流大小都保持不变的端电压。正确的端电压是 V = ε − Ir。在电路中，若外电阻减小，电流增大，内电压 Ir 升高，端电压 V 就会下降——这就是电池重载时电压显得“没电”的原因。
A typical graph‑based problem gives V against I. The y‑intercept is the emf ε, and the negative gradient’s magnitude is the internal resistance r. Watch out: if axes are swapped, the gradient changes. Also, a zero‑current voltmeter reading gives ε, not terminal voltage under load.
典型的图线题给出 V – I 图像：y 轴截距就是电动势 ε，斜率的绝对值即为内阻 r。注意，如果坐标轴对调，斜率含义会改变。另外，用伏特计在断路时测得的电压是电动势 ε，而不是有负载时的端电压。
6. Projectile Motion: Independent Components | 抛体运动：独立分解
Many mistakes come from mixing horizontal and vertical components. Horizontally, velocity is constant (ignoring air resistance); vertically, there is constant acceleration g downwards. At the peak, vertical velocity is zero, but horizontal velocity is unchanged, so the instantaneous speed is not zero. Similarly, acceleration is always g downwards, never zero at any point.
许多错误源于混淆水平与竖直分量。水平方向上速度恒定（忽略空气阻力）；竖直方向上存在恒定向下的加速度 g。在最高点，竖直分速度为零，但水平分速度保持不变，因此瞬时速率并不为零。同样，任何一点的加速度始终是向下的 g，绝无为零的时刻。
Symmetry in projectile motion is valid only when launch and landing are at the same height. The time to go up equals the time to come down, and the speed at a given height is the same on the way up and down. However, if the projectile lands lower or higher, these symmetries break. Always split initial velocity into components using uₓ = u cosθ, uᵧ = u sinθ.
抛体运动的对称性仅在起落点高度相同时成立。上升时间等于下降时间，在同一高度处上升和下降的速率相等。然而，若落点较低或较高，这些对称性便不再成立。总是要把初速度分解为水平分量 uₓ = u cosθ 和竖直分量 uᵧ = u sinθ。
7. Sign Conventions in the First Law of Thermodynamics | 热力学第一定律的符号规则
The first law ΔU = Q + W (or sometimes ΔU = Q − W) causes endless confusion because different syllabuses use different sign conventions. In IB and many WJEC contexts, ΔU = Q + W, where W is work done ON the gas. If work is done BY the gas, W is negative. Students must check the convention stated in the question; never assume.
热力学第一定律 ΔU = Q + W（有时写为 ΔU = Q − W）之所以令人头疼，是因为不同课程体系采用的符号规则不一致。在 IB 和许多 WJEC 的题目中，常见形式为 ΔU = Q + W，其中 W 表示对气体做的功。如果气体对外做功，W 就是负值。考生务必看清题目中给出的约定，不可想当然。
Common slip: in an adiabatic compression, Q = 0, work is done ON the gas, so W > 0, hence ΔU > 0 and temperature rises. In an isothermal expansion, ΔU = 0, so Q = −W (if W is work done on gas, then W is negative, Q positive — heat absorbed). Practice with p–V diagrams to correctly identify work done as area under the curve.
常见疏忽：在绝热压缩中，Q = 0，外界对气体做正功，W > 0，因此 ΔU > 0，温度升高。在等温膨胀中，ΔU = 0，所以 Q = −W（若 W 为对气体做功，则 W 为负，Q 为正，表示吸热）。结合 p–V 图练习，准确将曲线下的面积识别为功，才能牢固掌握。
8. Photoelectric Effect: Stopping Potential vs Intensity | 光电效应：截止电压与光强
A high‑frequency misconception: increasing the intensity of the incident light increases the kinetic energy of the emitted photoelectrons. In fact, the maximum kinetic energy Ek max = hf − φ depends only on the frequency f of the light and the work function φ of the metal. Intensity affects only the number of photons, and hence the photocurrent, not the maximum energy per electron. The stopping potential Vs is directly a measure of Ek max.
一个高频误区：增强入射光强可以增大逸出光电子的动能。事实上，最大动能 Ek max = hf − φ 只取决于光的频率 f 和金属的逸出功 φ。光强只影响光子数目，从而影响光电流的大小，而不改变单个电子的最大动能。截止电压 Vs 正是 Ek max 的直接量度。
Graph question: the Vs–f graph is a straight line with gradient h/e and x‑intercept equal to the threshold frequency f₀. Students sometimes read the threshold frequency incorrectly if line does not pass through origin. Also, if the metal is changed, the gradient stays the same (Planck’s constant is universal) but the intercept shifts.
图线题：Vs–f 图是一条直线，斜率是 h/e，横轴截距为截止频率 f₀。有时学生见直线不过原点就误读截止频率。另外，如果换了金属，斜率不变（普朗克常数是普适的），但截距会移动。
9. Lenz’s Law and Direction of Induced Current | 楞次定律与感应电流方向
Lenz’s law states that the direction of an induced emf is such that it opposes the change in magnetic flux that produces it. Many students remember ‘opposes’ but apply it to the wrong quantity. If a magnet’s north pole moves toward a coil, the induced current creates a north pole facing the magnet to repel it — opposing the approach, not the magnet itself. When the magnet is pulled away, the coil becomes a south pole to attract it, opposing the separation.
楞次定律指出，感应电动势的方向总是使其感应电流反抗引起它的磁通量变化。许多学生记住了“反抗”二字，却用错了对象。若磁体 N 极靠近线圈，感应电流产生的磁场在靠近磁体的一端应为 N 极，从而排斥磁体——反抗的是“靠近”这一变化，而非磁体本身。当磁体被拉远时，线圈该端变为 S 极以吸引它，反抗的是“远离”。
A frequent exam question involves a conducting loop moving into or out of a magnetic field. Students confuse the direction of magnetic force on induced charges with the direction of induced emf. Use the right‑hand rule for flux and force cautiously: first determine whether flux is increasing or decreasing, then decide the direction of the induced field that opposes the change, and finally use a grip rule to find induced current direction.
常考题型涉及导体回路移入或移出磁场。学生容易把感应电荷所受磁力方向与感应电动势方向弄混。要谨慎使用右手定则：先判断磁通量是增加还是减少，再确定反抗这一变化的感应磁场方向，最后用右手螺旋定则得到感应电流方向。
10. Standing Waves: Nodes, Antinodes and Energy | 驻波：波节、波腹与能量
In a stationary wave, energy is not transferred along the medium. This surprises students who see large amplitudes at antinodes. Actually, energy is trapped, oscillating between kinetic and potential forms locally. The net energy flow is zero. Nodes have zero displacement but maximum pressure variation in a sound tube — a common trick question. Understanding that nodes and antinodes swap between pressure and displacement graphs is vital.
在驻波中，能量并不沿介质传播。这一点常让看到腹点大幅振动却无能量传递的学生感到惊讶。实际上，能量被“困”住了，在动能和势能之间就地转换，净能量流为零。波节处位移为零，但在声管中压力变化最大——这是一道经典的陷阱题。关键在于分清压力驻波和位移驻波的波节、波腹恰好互换。
For a string fixed at both ends, the fundamental frequency corresponds to λ/2 = L, giving f₁ = v/(2L). The overtone patterns are often mislabelled: the second harmonic is the first overtone, with two loops. In closed pipes, only odd harmonics exist. Always draw a clear diagram and label nodes (N) and antinodes (A) before plugging numbers into the formula.
对于两端固定的弦，基频对应 λ/2 = L，即 f₁ = v/(2L)。这些泛音模式常被标错：二次谐波就是第一泛音，有两个波腹。在闭管中，只有奇数倍的谐波存在。务必先画出清晰的示意图，标出波节 (N) 和波腹 (A)，再将数据代入公式计算。
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