📚 IB Physics: Core Concepts and Exam Points in Electromagnetism | IB物理：电磁学核心概念与考点梳理
Electromagnetism is one of the most conceptually rich and exam-relevant topics in IB Physics. It unifies electric and magnetic phenomena through the concept of fields, and it underpins countless applications from capacitors to generators. This article provides a structured review of the core ideas, key equations, and common exam traps you must master for both SL and HL.
电磁学是IB物理中概念最丰富、考点最密集的板块之一。它通过“场”的概念将电与磁现象统一起来，并支撑着从电容器到发电机等无数应用。本文旨在系统梳理核心概念、关键方程与常见易错点，帮助你在SL和HL阶段都能精准掌握考点。
1. Electric Charge and Coulomb’s Law | 电荷与库仑定律
Electric charge is a fundamental property of matter. Like charges repel, unlike charges attract. The SI unit of charge is the coulomb (C), and the elementary charge is e = 1.60 × 10⁻¹⁹ C.
电荷是物质的基本属性。同种电荷相斥，异种电荷相吸。电荷的国际单位是库仑（C），元电荷为 e = 1.60 × 10⁻¹⁹ C。
Coulomb’s law gives the force between two point charges:
库仑定律给出了两个点电荷之间的作用力：
F = k|q₁q₂| / r² = (1 / 4πε₀) · |q₁q₂| / r²
·m⁻² is the permittivity of free space. The force acts along the line joining the charges.
其中 k ≈ 8.99 × 10⁹ N·m²·C⁻²，ε₀ = 8.85 × 10⁻¹² C²·N⁻¹·m⁻² 是真空介电常数。力的方向沿两电荷连线。
- IB exam tip: Always state whether the force is attractive or repulsive; do not just give a magnitude.
- IB考试提示：在描述库仑力时一定要说明是引力还是斥力，不能只写大小。
2. Electric Field and Field Lines | 电场与电场线
An electric field is a region where a charge experiences a force. The electric field strength E at a point is defined as the force per unit positive charge: E = F/q. Its unit is N·C⁻¹ or V·m⁻¹.
电场是电荷在其中会受到力的空间区域。电场强度 E 定义为每单位正电荷所受的力：E = F/q，单位是 N·C⁻¹ 或 V·m⁻¹。
For a point charge Q, the field strength at distance r is:
对于点电荷 Q，距离 r 处的场强为：
E = kQ / r²
Electric field lines start on positive charges and end on negative charges. The density of lines indicates the strength of the field. In a uniform field, the lines are parallel and equally spaced.
电场线从正电荷出发，终止于负电荷。电场线的疏密表示场强大小。在匀强电场中，电场线平行且间距相等。
For a uniform field between two parallel plates separated by distance d with potential difference V:
对于间距为 d、电势差为 V 的两平行板之间的匀强电场：
E = V / d
- Remember: Field strength is a vector; use superposition for multiple charges.
- 注意：场强是矢量；多个电荷时需用叠加原理。
3. Electric Potential and Potential Difference | 电势与电势差
Electric potential V at a point is the work done per unit charge in bringing a positive test charge from infinity to that point. For a point charge Q:
电场中某点的电势 V 是将单位正电荷从无穷远处移到该点所做的功。对于点电荷 Q：
V = kQ / r
Potential difference (voltage) ΔV between two points is the work done per unit charge moving a charge between those points: W = qΔV.
两点之间的电势差（电压）ΔV 是单位电荷在两点间移动时所做的功：W = qΔV。
Equipotential surfaces are surfaces of constant potential. In a uniform field, they are planes perpendicular to the field lines. No work is done moving a charge along an equipotential surface.
等势面是电势相等的面。在匀强电场中，等势面是与电场线垂直的平面。电荷沿等势面移动时电场力不做功。
- Common misconception: Potential is zero at infinity is a convention; only differences matter in calculations.
- 常见误区：电势“无穷远处为零”只是约定；实际计算中只有电势差才有意义。
4. Capacitance and Energy Storage | 电容与储能
A capacitor stores charge and energy. Capacitance C is defined as C = Q/V, where Q is the magnitude of charge on either plate and V is the potential difference between the plates. The unit is the farad (F).
电容器储存电荷和能量。电容 C 定义为 C = Q/V，其中 Q 是任一极板上的电荷量，V 是两极板间的电势差。单位是法拉（F）。
For a parallel-plate capacitor in a vacuum, capacitance depends on geometry:
真空中的平行板电容器，其电容取决于几何结构：
C = ε₀A / d
Where A is the plate area and d is the separation. If a dielectric of relative permittivity εᵣ fills the gap, multiply by εᵣ.
其中 A 是极板面积，d 是极板间距。若两极板间充满相对介电常数为 εᵣ 的电介质，则电容要乘以 εᵣ。
The energy stored in a charged capacitor is:
充电电容器储存的能量为：
E = ½ QV = ½ CV² = Q² / (2C)
- HL requirement: Understand how inserting a dielectric changes C, Q, V, and stored energy in constant-voltage vs. isolated-capacitor cases.
- HL要求：理解在恒压或孤立电容器情形下，插入电介质如何改变 C、Q、V 和储能。
5. Electric Current and Ohm’s Law | 电流与欧姆定律
Electric current is the rate of flow of charge. The average current is I = ΔQ/Δt. Conventional current direction is from positive to negative, opposite to electron flow.
电流是电荷流动的速率。平均电流为 I = ΔQ/Δt。规定电流方向是从正极到负极，与电子运动方向相反。
Ohm’s law states that for an ohmic conductor at constant temperature, the potential difference V across it is proportional to the current I through it:
欧姆定律指出，对于温度恒定的欧姆导体，其两端电压 V 与通过它的电流 I 成正比：
V = IR
Resistance R depends on the material and geometry: R = ρL / A, where ρ is resistivity, L is length, and A is cross-sectional area. Resistivity is temperature-dependent; for metals it increases with temperature.
电阻 R 取决于材料和几何形状：R = ρL / A，其中 ρ 是电阻率，L 是长度，A 是横截面积。电阻率随温度变化；金属的电阻率随温度升高而增大。
- I–V characteristic curves: a straight line through the origin for ohmic conductors; curves for filament lamps, diodes, and thermistors.
- I–V 特性曲线：欧姆导体为过原点的直线；白炽灯、二极管、热敏电阻则呈现曲线。
6. DC Circuits and Kirchhoff’s Laws | 直流电路与基尔霍夫定律
Real circuits consist of resistors, cells, and connecting wires. A cell has an internal resistance r, so the terminal voltage is less than the emf when current flows: V_terminal = ε − Ir.
实际电路由电阻、电池和导线组成。电池有内阻 r，因此当有电流流过时，路端电压小于电动势：V_terminal = ε − Ir。
For series resistors: Rtotal = R₁ + R₂ + R₃ + ...
串联电阻：Rtotal = R₁ + R₂ + R₃ + ...
For parallel resistors:
并联电阻：
1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...
Kirchhoff’s laws are powerful tools for complex circuits:
基尔霍夫定律是分析复杂电路的有力工具：
- Kirchhoff’s current law (KCL): The sum of currents entering any junction equals the sum leaving it (charge conservation).
- 基尔霍夫电流定律（KCL）：流入任一节点的电流之和等于流出该节点的电流之和（电荷守恒）。
- Kirchhoff’s voltage law (KVL): The sum of emfs around any closed loop equals the sum of potential drops (energy conservation).
- 基尔霍夫电压定律（KVL）：沿任一闭合回路，电动势之和等于电势降之和（能量守恒）。
7. Magnetic Fields and Magnetic Force | 磁场与磁场力
Magnetic fields are produced by moving charges or permanent magnets. The magnetic field strength (magnetic flux density) B is measured in tesla (T). Field lines point from north to south outside a magnet.
磁场由运动的电荷或永磁体产生。磁感应强度（磁通密度）B 的单位是特斯拉（T）。磁场线在磁体外部从 N 极指向 S 极。
A charge q moving with velocity v perpendicular to a uniform magnetic field B experiences a force:
当电荷 q 以速度 v 垂直于匀强磁场 B 运动时，受到的磁场力为：
F = qvB
For an arbitrary angle θ between v and B, F = qvB sinθ. The direction is given by the right-hand rule for a positive charge. This force is always perpendicular to the velocity, so it does no work and changes only the direction of motion.
若 v 与 B 的夹角为 θ，则 F = qvB sinθ。方向由右手定则确定（针对正电荷）。该力始终垂直于速度，因此不做功，只改变运动方向。
For a current-carrying wire of length L in a uniform magnetic field, the force is:
对于处在匀强磁场中、长度为 L 的通电导线，所受磁场力为：
F = BIL sinθ
- motion of a charged particle in a perpendicular magnetic field, with radius r = mv / (qB).
- 常见考题：带电粒子在垂直磁场中做匀速圆周运动，半径 r = mv / (qB)。
8. Electromagnetic Induction and Faraday’s Law | 电磁感应与法拉第定律
Electromagnetic induction occurs when the magnetic flux through a circuit changes. Magnetic flux Φ through an area A in a field B is defined as Φ = BA cosθ, where θ is the angle between the field direction and the normal to the area. The unit is the weber (Wb).
当穿过回路的磁通量发生变化时，就会产生电磁感应。磁通量 Φ 定义为 Φ = BA cosθ，其中 θ 是磁场方向与面积法线方向的夹角，单位是韦伯（Wb）。
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 (ΔΦ / Δt)
Here N is the number of turns, and NΦ is the flux linkage. Lenz’s law gives the direction: the induced current opposes the change that produced it. The negative sign in Faraday’s law reflects Lenz’s law.
其中 N 是线圈匝数，NΦ 是磁通链。楞次定律给出感应电流的方向：感应电流总是阻碍引起它的磁通量变化。法拉第定律中的负号正体现了楞次定律。
- : HL requires using the derivative form ε = −d(NΦ)/dt and explaining motional emf ε = BvL.
- SL/HL区别：HL要求使用导数形式 ε = −d(NΦ)/dt，并能解释动生电动势 ε = BvL。
9. Alternating Current and Transformers | 交流电与变压器
Alternating current (AC) varies sinusoidally with time: I = I₀ sin(ωt) and V = V₀ sin(ωt). The root-mean-square (rms) values are used for power calculations:
交流电随时间按正弦规律变化：I = I₀ sin(ωt)、V = V₀ sin(ωt)。计算功率时使用有效值（rms）：
Vrms = V₀ / √2, Irms = I₀ / √2
Average power dissipated in a resistor is P = Vrms Irms = Irms²R = Vrms²/R.
电阻上消耗的平均功率为 P = Vrms Irms = Irms²R = Vrms²/R。
An ideal transformer steps voltage up or down using mutual induction:
理想变压器利用互感升压或降压：
Vs / Vp = Ns / Np
For an ideal transformer, input power equals output power: Vp Ip = Vs Is. Power losses in real transformers are reduced by laminated iron cores, thick low-resistance wires, and efficient designs to minimize eddy currents and hysteresis.
理想变压器输入功率等于输出功率：Vp Ip = Vs Is。实际变压器的功率损耗通过使用叠片铁芯、低电阻粗导线以及抑制涡流和磁滞损耗的设计来减小。
10. Common Exam Traps and How to Avoid Them | 常见考试陷阱与应对策略
Many students lose marks on electromagnetism not because they lack knowledge, but because of small conceptual slips. Here are the most frequent traps.
许多学生在电磁学上失分并非因为知识不足，而是因为一些小的概念性疏漏。以下是最高频的陷阱。
- N/C) with electric potential V (J/C). They are related by E = ΔV/d only in uniform fields.
- 陷阱1：混淆电场强度 E（N/C）与电势 V（J/C）。只有在匀强电场中它们才满足 E = ΔV/d。
- Trap 2: Forgetting that the magnetic force does no work. A charged particle in a magnetic field changes direction but not speed.
- 陷阱2：忘记磁场力不做功。带电粒子在磁场中只改变方向，不改变速率。
- Trap 3: Using the wrong rms vs. peak values. Power must be calculated with rms values in AC circuits.
- 陷阱3：混用有效值与峰值。交流电路中计算功率必须使用有效值。
- Trap 4: Ignoring internal resistance. Terminal voltage is not the same as emf except at open circuit.
- 陷阱4：忽略内阻。除了断路情况，路端电压不等同于电动势。
- Trap 5: Misapplying Lenz’s law. Always ask: “Does the induced current oppose the change in flux?” Then find the direction.
- 陷阱5：错误应用楞次定律。始终问自己：“感应电流是否阻碍了磁通量的变化？”然后判断方向。
To score high, practice drawing field lines, labeling directions, and writing symbolic answers before substituting numbers. Review past paper questions on circuits and induction until the patterns become automatic.
要想拿高分，请多练习画电场线/磁场线、标注方向，并养成先写出符号表达式再代入数值的习惯。反复做历年真题中关于电路和感应部分的题目，直到熟悉所有常见题型。
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