📚 IB Physics: Core Concepts of Electromagnetism | IB物理：电磁学核心概念梳理
Electromagnetism is one of the most important topics in IB Physics, bringing together electric fields, magnetic fields, and their dynamic interplay. This article provides a clear, exam-focused review of the core concepts you need to master for both Standard Level (SL) and Higher Level (HL).
电磁学是IB物理中最重要的主题之一，它将电场、磁场及二者之间的动态相互作用紧密联系在一起。本文将为SL和HL学生提供一份清晰、紧扣考点的核心概念梳理，帮助你高效复习。
1. Electric Charge and Coulomb's Law | 电荷与库仑定律
rge is e = 1.60 × 10⁻¹⁹ C. Charges of the same sign repel, while opposite charges attract.
电荷是物质的基本属性。电荷的国际单位是库仑（C），元电荷为 e = 1.60 × 10⁻¹⁹ C。同种电荷相互排斥，异种电荷相互吸引。
Coulomb's law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
库仑定律表明：两个点电荷之间的静电力大小与电荷量的乘积成正比，与它们之间距离的平方成反比。
F = k |q₁q₂| / r² = (1 / 4π ε₀) |q₁q₂| / r²
·N⁻¹·m⁻² is the permittivity of free space. The force acts along the line joining the two charges.
其中 k = 8.99 × 10⁹ N·m²·C⁻² 为库仑常量，ε₀ = 8.85 × 10⁻¹² C²·N⁻¹·m⁻² 为真空介电常数。力的方向沿两电荷的连线。
For multiple charges, use the principle of superposition: the net force on one charge is the vector sum of forces from all other charges.
对多个电荷，使用叠加原理：某一电荷所受合力是其他各电荷单独作用力的矢量和。
Coulomb's law applies only to point charges or spherically symmetric charge distributions.
库仑定律仅适用于点电荷或球对称分布的电荷。
2. Electric Field Strength and Field Lines | 电场强度与电场线
An electric field exists in the region around a charge, and it exerts a force on other charges placed within it. The electric field strength E at a point is defined as the force per unit positive charge placed at that point.
电场存在于电荷周围的区域，并对放入其中的其他电荷施加力的作用。电场强度 E 定义为置于该点的单位正电荷所受的力。
E = F / q
The unit of electric field strength is N·C⁻¹ or V·m⁻¹. For a point charge Q, the field strength at a distance r is given by:
电场强度的单位是 N·C⁻¹ 或 V·m⁻¹。对于点电荷 Q，距离 r 处的场强为：
E = kQ / r² = (1 / 4π ε₀) Q / r²
Electric field lines are a visual representation of the field. They point away from positive charges and toward negative charges. The density of field lines indicates the magnitude of the field, and lines never cross each other.
电场线是电场的可视化表示。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，电场线永不相交。
s approximately constant, E = V / d, where V is the voltage and d is the plate separation.
匀强电场：两块平行板之间电场近似均匀，E = V / d，其中 V 为电压，d 为板间距。
3. Electric Potential and Potential Difference | 电势与电势差
Electric potential V at a point in an electric field is defined as the work done per unit charge in bringing a positive test charge from infinity to that point.
电场中某点的电势 V 定义为单位正电荷从无穷远处移到该点过程中电场力所做的功。
V = W / q
For a point charge Q, the potential at distance r is:
对于点电荷 Q，距离 r 处的电势为：
V = kQ / r = (1 / 4π ε₀) Q / r
elationship between electric field and potential difference in a uniform field is ΔV = Ed.
电势差（电压）是移动单位电荷在两点之间时所做的功。在匀强电场中，场强与电势差的关系为 ΔV = Ed。
equals the energy gained by an electron accelerated through a potential difference of 1 V.
电子伏特（eV）是能量单位：1 eV = 1.60 × 10⁻¹⁹ J。它等于电子通过1 V电势差加速后获得的能量。
Equipotential surfaces are always perpendicular to electric field lines.
等势面总是与电场线垂直。
4. Magnetic Fields and Magnetic Force | 磁场与磁力
A magnetic field is a region where a moving charge or a magnetic dipole experiences a force. The magnetic field strength, also called magnetic flux density, is denoted by B and measured in tesla (T).
磁场是运动的电荷或磁偶极子受到力的作用的区域。磁场强度，也称为磁感应强度，用 B 表示，单位为特斯拉（T）。
Magnetic forces act only on moving charges. For a charge q moving with velocity v perpendicular to a magnetic field B, the force is given by:
磁场力只作用于运动电荷。当电荷 q 以速度 v 垂直于磁场 B 运动时，受力为：
F = qvB sin θ
where θ is the angle between v and B. The direction of the force is given by the right-hand rule (or Fleming's left-hand rule for conventional current).
其中 θ 是 v 与 B 之间的夹角。力的方向由右手定则（或对电流使用左手定则）确定。
e is zero. When v is perpendicular to B, the motion is circular with radius r = mv / (qB).
当 v 平行于 B 时，磁场力为零。当 v 垂直于 B 时，做圆周运动，半径 r = mv / (qB)。
The magnetic force does no work on a charged particle because it is always perpendicular to the velocity.
磁场力对带电粒子不做功，因为它始终垂直于速度方向。
5. Magnetic Force on a Current-Carrying Conductor | 电流在磁场中的安培力
When a current flows through a wire placed in a magnetic field, the moving charges within the wire experience a magnetic force. The total force on a straight wire of length L carrying current I in a uniform magnetic field B is:
当通电导线置于磁场中时，导线内的运动电荷会受到磁场力。长度为 L 的直导线通有电流 I，在匀强磁场 B 中所受合力为：
F = BIL sin θ
een the wire and the magnetic field. When the wire is perpendicular to the field, F = BIL.
其中 θ 为导线与磁场方向的夹角。当导线垂直于磁场时，F = BIL。
This principle is the basis of electric motors and loudspeakers.
该原理是电动机和扬声器的基础。
Two parallel current-carrying wires attract if currents are in the same direction and repel if currents are opposite.
两根平行通电导线中，电流同向时相互吸引，反向时相互排斥。
6. Magnetic Fields Produced by Currents | 电流产生的磁场
Oersted discovered that an electric current produces a magnetic field around it. The magnetic field around a long straight wire is circular, with its magnitude given by Ampère's law for a wire:
奥斯特发现电流可以在周围产生磁场。长直导线周围的磁场呈环形分布，其大小由安培定律给出：
B = μ₀I / (2π r)
4π × 10⁻⁷ T·m·A⁻¹ is the permeability of free space, and r is the distance from the wire.
其中 μ₀ = 4π × 10⁻⁷ T·m·A⁻¹ 为真空磁导率，r 为到导线的距离。
For a solenoid, the magnetic field inside is nearly uniform and is given by:
对于螺线管，其内部磁场近似均匀，大小为：
B = μ₀nI
where n is the number of turns per unit length and I is the current.
其中 n 为单位长度的匝数，I 为电流。
The right-hand grip rule determines the direction of the magnetic field around a current-carrying wire.
右手螺旋定则用于判断通电导线周围磁场的方向。
7. Electromagnetic Induction and Faraday's Law | 电磁感应与法拉第定律
Electromagnetic induction occurs when a changing magnetic flux through a circuit induces an electromotive force (emf). The magnetic flux Φ through a surface is defined as:
当通过电路的磁通量发生变化时，会产生感应电动势，这就是电磁感应。穿过某一面积的磁通量 Φ 定义为：
Φ = BA cos θ
ld and the normal to the surface. The unit of flux is the weber (Wb), where 1 Wb = 1 T·m².
其中 θ 是磁场方向与面法线方向之间的夹角。磁通量的单位是韦伯（Wb），1 Wb = 1 T·m²。
Faraday's law states that the induced emf is equal to the negative rate of change of magnetic flux:
法拉第定律表明：感应电动势等于磁通量变化率的负值：
ε = −N dΦ / dt
where N is the number of turns in the coil. The negative sign is a consequence of Lenz's law.
其中 N 是线圈匝数。负号是楞次定律的结果。
8. Lenz's Law and Conservation of Energy | 楞次定律与能量守恒
Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This is a direct consequence of the conservation of energy.
楞次定律指出：感应电流的方向总是阻碍引起它的磁通量变化。这是能量守恒定律的直接结果。
If the magnetic flux through a coil increases, the induced current creates a magnetic field opposing the increase.
如果线圈中的磁通量增加，感应电流产生的磁场会阻碍这种增加。
If the flux decreases, the induced current creates a field that supports the original field.
如果磁通量减少，感应电流产生的磁场会维持原来的磁场。
Lenz's law explains why mechanical work must be done to move a magnet into and out of a coil: the electrical energy generated comes from the mechanical work done, ensuring energy conservation.
楞次定律解释了为什么将磁铁插入或拔出线圈时需要做机械功：产生的电能来自所做的机械功，从而保证能量守恒。
9. Alternating Current and Transformers | 交流电与变压器
Alternating current (AC) is an electric current that periodically reverses direction. The standard AC voltage in many countries is sinusoidal, described by:
交流电（AC）是方向周期性变化的电流。许多国家的标准交流电压呈正弦波形式，可表示为：
V = V₀ sin(2π f t)
where V₀ is the peak voltage and f is the frequency. The root-mean-square (rms) value is Vrms = V₀ / √2.
其中 V₀ 为峰值电压，f 为频率。有效值（均方根值）为 Vrms = V₀ / √2。
Transformers use electromagnetic induction to change the voltage of AC. For an ideal transformer:
变压器利用电磁感应改变交流电压。对于理想变压器：
Vₚ / Vₛ = Nₚ / Nₛ
where subscript p refers to the primary coil and s to the secondary coil.
其中下标 p 表示原线圈，s 表示副线圈。
Step-up transformers increase voltage and decrease current; step-down transformers do the reverse.
升压变压器升高电压并降低电流；降压变压器则相反。
Power loss in transmission lines is reduced by transmitting at high voltage, since Ploss = I²R.
输电线路中的功率损耗通过高压传输来减少，因为 Ploss = I²R。
10. Capacitance and Dielectrics | 电容与电介质
A capacitor stores electrical energy in an electric field. The capacitance C is defined as the charge stored per unit potential difference:
电容器以电场形式储存电能。电容 C 定义为单位电势差所储存的电荷量：
C = Q / V
The unit of capacitance is the farad (F). For a parallel-plate capacitor, the capacitance is given by:
电容的单位是法拉（F）。对于平行板电容器，电容为：
C = ε₀εᵣ A / d
where A is the plate area, d is the separation, and εᵣ is the relative permittivity (dielectric constant) of the material between the plates.
其中 A 为极板面积，d 为极板间距，εᵣ 为极板间材料的相对介电常数（介电常数）。
When a dielectric is inserted, capacitance increases because the dielectric reduces the electric field within the capacitor.
插入电介质后电容增大，因为电介质削弱了电容器内部的电场。
11. Energy Stored in Electric and Magnetic Fields | 电场与磁场中储存的能量
An electric field stores energy. The energy stored in a capacitor charged to voltage V is:
电场储存能量。电容器充电至电压 V 时储存的能量为：
E = ½ CV² = ½ QV = Q² / (2C)
Similarly, a magnetic field stores energy. For an inductor carrying current I, the stored energy is:
类似地，磁场也储存能量。对于通有电流 I 的电感器，储存的能量为：
E = ½ LI²
where L is the inductance measured in henry (H).
其中 L 为电感，单位是亨利（H）。
Energy density in an electric field: u = ½ ε₀E²
电场的能量密度：u = ½ ε₀E²
Energy density in a magnetic field: u = B² / (2μ₀)
磁场的能量密度：u = B² / (2μ₀)
12. Electromagnetic Waves | 电磁波
Electromagnetic waves are produced by accelerating charges. They consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation.
电磁波由加速运动的电荷产生。它们由相互垂直、且垂直于传播方向的振荡电场和磁场组成。
In free space, electromagnetic waves travel at the speed of light:
在真空中，电磁波的传播速度为光速：
c = 1 / √μ₀ε₀ = 3.00 × 10⁸ m·s⁻¹
The wavelength λ and frequency f of an electromagnetic wave are related by:
电磁波的波长 λ 与频率 f 的关系为：
c = f λ
The electromagnetic spectrum includes, from low to high frequency: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
电磁波谱从低到高频依次包括：无线电波、微波、红外线、可见光、紫外线、X射线和伽马射线。
Electromagnetic waves transfer energy and momentum; they do not require a medium.
电磁波传递能量和动量，不需要介质传播。
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