Edexcel A-Level Physics Topic 7: Electric and Magnetic Fields | 爱德思 A-Level 物理第7章：电场与磁场

📚 Edexcel A-Level Physics Topic 7: Electric and Magnetic Fields | 爱德思 A-Level 物理第7章：电场与磁场

Electric and magnetic fields are central to Topic 7 of Edexcel A-Level Physics. This unit links electric charge, electric potential energy, capacitance, magnetic forces and electromagnetic induction. Mastering it builds the foundation for understanding capacitors, particle accelerators, motors and generators.

电场与磁场是爱德思 A-Level 物理第 7 章的核心内容。本单元将电荷、电势能、电容、磁场力和电磁感应联系在一起。掌握本章可为理解电容器、粒子加速器、电动机和发电机打下坚实基础。

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1. Overview: From Charges to Applications | 概览：从电荷到应用

In Topic 7, Edexcel brings together electric fields, capacitors, magnetic fields and electromagnetic induction. The key idea is that a field is a region where a charge or current experiences a non-contact force.

在第 7 章中，爱德思将电场、电容器、磁场和电磁感应结合在一起。核心思想是：场是一个区域，其中电荷或电流会受到非接触力。

Electric fields act on charged particles, while magnetic fields act on moving charges and current-carrying conductors. Combining these fields allows devices such as velocity selectors and mass spectrometers to control charged particles precisely.

电场作用于带电粒子，磁场作用于运动电荷和载流导体。将电场和磁场组合起来，可以让速度选择器和质谱仪等设备精确控制带电粒子。

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2. Electric Field Strength and Coulomb’s Law | 电场强度与库仑定律

Electric field strength E is defined as the force per unit positive charge:

电场强度 E 定义为单位正电荷所受的力：

E = F / Q

The unit of E is N C⁻¹, which is equivalent to V m⁻¹. The direction of an electric field is the direction of the force on a positive test charge.

E 的单位是 N C⁻¹，也等于 V m⁻¹。电场的方向就是正检验电荷所受力的方向。

For two point charges, the force between them is given by Coulomb’s law:

两个点电荷之间的力由库仑定律给出：

F = kQ₁Q₂ / r²

where k = 1 / (4πε₀) ≈ 8.99 × 10⁹ N m² C⁻², and ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹. This gives the radial electric field around a point charge.

其中 k = 1 / (4πε₀) ≈ 8.99 × 10⁹ N m² C⁻²，ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹。这就是点电荷周围的径向电场。

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3. Uniform Electric Fields and Potential Difference | 匀强电场与电势差

A uniform electric field is produced between two parallel charged plates. The field strength is constant and related to the potential difference V and plate separation d:

两块平行带电板之间会产生匀强电场。场强恒定，并且与电势差 V 和板间距 d 有关：

E = V / d

This equation only applies to a uniform field. The work done W on a charge Q moving through a potential difference V is W = QV. This leads to the electron-volt: 1 eV = 1.60 × 10⁻¹⁹ J.

该公式仅适用于匀强电场。电荷 Q 经过电势差 V 时所做的功为 W = QV。由此引出电子伏特：1 eV = 1.60 × 10⁻¹⁹ J。

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4. Electric Potential and Electrical Energy | 电势与电势能

Electric potential V at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. For a radial field around a point charge Q:

某点的电势 V 是将单位正检验电荷从无穷远处移到该点所做的功。对于点电荷 Q 周围的径向电场：

V = kQ / r

Electric potential is a scalar, so the sign of V follows the sign of the source charge. The electric potential energy of a charge q at that point is U = qV.

电势是标量，因此 V 的正负与源电荷的正负一致。电荷 q 在该点的电势能为 U = qV。

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5. Capacitance: Storing Charge and Energy | 电容：储存电荷与能量

Capacitance C is defined as the charge stored per unit potential difference:

电容 C 定义为单位电势差下储存的电荷量：

C = Q / V

The unit of capacitance is the farad F. For a parallel-plate capacitor, the capacitance depends on the plate area A and separation d:

电容的单位是法拉 F。对于平行板电容器，电容取决于板面积 A 和板间距 d：

C = ε₀A / d

Adding a dielectric increases capacitance by a factor εᵣ, where εᵣ is the relative permittivity. The energy stored in a capacitor can be expressed in three equivalent forms:

加入电介质会使电容增大 εᵣ 倍，其中 εᵣ 是相对介电常数。电容器储存的能量有三种等价表达式：

E = ½ QV = ½ CV² = ½ Q² / C

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6. Magnetic Flux Density and Forces on Currents | 磁通密度与电流受力

Magnetic flux density B is measured in tesla T. The force on a straight current-carrying conductor in a magnetic field is:

磁通密度 B 的单位是特斯拉 T。磁场中直载流导体所受的力为：

F = BIL sin θ

where I is the current, L is the length of the conductor in the field and θ is the angle between the conductor and the field lines. The force is greatest when θ = 90° and zero when θ = 0°.

其中 I 是电流，L 是导体在磁场中的长度，θ 是导体与磁感线之间的夹角。θ = 90° 时力最大，θ = 0° 时力为零。

For a single moving charge, the magnetic force is:

对于单个运动电荷，磁场力为：

F = Bqv sin θ

Fleming’s left-hand rule gives the direction: thumb for force, first finger for magnetic field, second finger for conventional current. For a negative charge

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