IB Physics: Core Concepts and Exam Points in Electromagnetism | IB物理：电磁学核心概念与考点梳理

📚 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

Here, k ≈ 8.99 × 10⁹ N·m²·C⁻², and ε₀ = 8.85 × 10⁻¹² C²·N⁻¹·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: R_total = R₁ + R₂ + R₃ + …

串联电阻：R_total = R₁ + R₂ + R₃ + …

For parallel resistors:

并联电阻：

1/R_total = 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

Common exam question: circular 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。

SL/HL distinction: 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）：

V_rms = V₀ / √2, I_rms = I₀ / √2

Average power dissipated in a resistor is P = V_rms I_rms = I_rms²R = V_rms²/R.

电阻上消耗的平均功率为 P = V_rms I_rms = I_rms²R = V_rms²/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：

V_s / V_p = N_s / N_p

For an ideal transformer, input power equals output power: V_p I_p = V_s I_s. 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：V_p I_p = V_s I_s。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。

Trap 1: Confusing electric field E (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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IB Physics: Core Concepts and Exam Points in Electromagnetism | IB物理：电磁学核心概念与考点梳理