📚 A-Level Physics: Attraction and Repulsion Between Charges | A-Level 物理：电荷间吸引与排斥作用
Electric charge is a fundamental property of matter that gives rise to electric forces. These forces can be attractive or repulsive depending on the signs of the charges involved. Understanding how charges interact is essential for mastering electrostatics in A-Level Physics.
电荷是物质的基本属性，它产生电场力。这些力可以是吸引力或排斥力，取决于所涉及电荷的正负。理解电荷如何相互作用，是掌握A-Level物理静电学部分的关键。
1. Electric Charges and Their Properties | 电荷及其基本性质
There are two types of electric charge: positive and negative. Protons carry a positive charge while electrons carry a negative charge. In a neutral atom, the number of protons equals the number of electrons.
电荷有两种：正电荷和负电荷。质子带正电，电子带负电。在电中性原子中，质子数等于电子数。
The SI unit of charge is the coulomb (C). One electron has a charge of -1.6 × 10⁻¹⁹ C, and one proton has +1.6 × 10⁻¹⁹ C.
电荷的国际单位是库仑（C）。一个电子所带电荷为 -1.6 × 10⁻¹⁹ C，一个质子为 +1.6 × 10⁻¹⁹ C。
Like charges repel each other; unlike charges attract each other. This fundamental rule explains many electrostatic phenomena, from the attraction of a balloon to hair to the operation of a photocopier.
同种电荷相互排斥，异种电荷相互吸引。这一基本规律解释了许多静电现象，从气球吸引头发到复印机的工作过程。
2. Coulomb’s Law | 库仑定律
For two point charges Q₁ and Q₂ separated by distance r, the magnitude of the electrostatic force between them is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
对于两个相距r的点电荷Q₁和Q₂，它们之间的静电力大小与电荷量乘积成正比，与距离的平方成反比。
F = k × |Q₁Q₂| / r²
where k is the Coulomb constant, k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²·C⁻². The force acts along the line joining the two charges.
其中k为库仑常量，k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²·C⁻²。力的方向沿两电荷连线。
If the charges have the same sign, the force is repulsive; if they have opposite signs, the force is attractive. According to Newton’s third law, the force on Q₁ due to Q₂ is equal in magnitude and opposite in direction to the force on Q₂ due to Q₁.
若两电荷同号，则作用力为斥力；若异号，则为引力。根据牛顿第三定律，Q₁所受Q₂的力与Q₂所受Q₁的力等大反向。
3. Quantisation and Conservation of Charge | 电荷的量子化与守恒
Charge is quantised: every observable charge is an integer multiple of the elementary charge e = 1.6 × 10⁻¹⁹ C. Thus Q = ±ne, where n is a positive integer.
电荷是量子化的：任何可观测电荷都是元电荷e = 1.6 × 10⁻¹⁹ C的整数倍，即Q = ±ne，其中n为正整数。
Charge is also conserved in an isolated system. The total electric charge before a process equals the total charge after the process. For example, in beta decay a neutron converts to a proton and an electron, preserving total charge.
在孤立系统中电荷守恒。一个过程前后的总电荷量不变。例如，β衰变中一个中子转变为质子和电子，总电荷保持不变。
When two objects are rubbed together, electrons may transfer from one to the other, making them oppositely charged. The total charge of the system remains zero.
当两个物体相互摩擦时，电子可能从一个物体转移到另一个物体，使二者带等量异种电荷，但系统的总电荷仍为零。
4. Electric Field Strength | 电场强度
The electric field at a point is defined as the force per unit positive charge placed at that point. Mathematically, E = F/q.
电场中某点的电场强度定义为放在该点的单位正电荷所受的力，即E = F/q。
For a point charge Q, the electric field at distance r is given by E = kQ/r². The direction of E is away from a positive charge and towards a negative charge.
对于点电荷Q，距离r处的电场强度为E = kQ/r²。电场方向从正电荷指向外，指向负电荷。
The unit of electric field strength is newton per coulomb (N/C), which is equivalent to volt per metre (V/m). This relationship helps calculate forces on other charges placed in the field: F = qE.
电场强度的单位是牛每库（N/C），也等价于伏每米（V/m）。该关系有助于计算场中其他电荷所受的力：F = qE。
5. Electric Field Lines | 电场线
Electric field lines are a visual representation of the electric field. They start on positive charges and end on negative charges. The density of lines indicates the field strength.
电场线是电场的可视化表示。电场线始于正电荷，终于负电荷。电场线的疏密表示场强大小。
Field lines never cross because the field has a unique direction at each point. They are closer together where the field is stronger.
电场线永不相交，因为每一点的场方向唯一。场强越大的地方，电场线越密集。
For a uniform electric field, the field lines are parallel and equally spaced. For attracting opposite charges, field lines connect them; for repelling like charges, the lines avoid each other and show a neutral region midway.
匀强电场的电场线是平行且等距的。对于相互吸引的异种电荷，电场线将它们连接；对于相互排斥的同种电荷，电场线彼此弯曲避开，并在中点附近出现中性区域。
6. Superposition of Forces and Fields | 力与场的叠加
When multiple charges are present, the net force on a charge is the vector sum of the individual forces due to each other charge. This is the principle of superposition.
当存在多个电荷时，某电荷所受合力等于其余每个电荷单独作用力的矢量和。这就是叠加原理。
Similarly, the electric field at a point due to several charges is the vector sum of the fields produced by each charge independently.
类似地，多个电荷在某点产生的合电场强度等于每个电荷独立产生的电场强度的矢量和。
For example, at a point on the perpendicular bisector of two equal positive charges, the horizontal components of the two fields cancel, while the vertical components add. The net field is along the perpendicular bisector.
例如，在两个等量正电荷连线的垂直平分线上的一点，两场强的水平分量相互抵消，垂直分量相加，合场强沿垂直平分线方向。
7. Electrostatic Induction and Polarisation | 静电感应与极化
Electrostatic induction occurs when a charged object is brought near a conductor, causing redistribution of charges. The near side acquires the opposite charge, and the far side acquires the same charge.
当带电体靠近导体时，会引起导体中电荷的重新分布，这就是静电感应。靠近带电体的一侧出现异种电荷，远端出现同种电荷。
If the conductor is then connected to the earth, the same charge on the far side can flow away, leaving the conductor with a net opposite charge. This process is called charging by induction.
如果此时将导体接地，远端的同种电荷可流入大地，使导体带上净异种电荷。这一过程称为感应起电。
In insulators, polarisation occurs. The molecules or atoms align so that the positive and negative charge centres shift slightly, leading to a weak attraction to any nearby charge.
在绝缘体中可发生极化。分子或原子内的正负电荷中心发生微小位移，从而对邻近电荷产生较弱吸引。
This explains why a charged balloon attracts small pieces of paper even though the paper is initially neutral.
这解释了为什么带电气球能吸引小纸片，即使纸片起初是中性的。
8. Motion of Charged Particles in a Uniform Electric Field | 带电粒子在匀强电场中的运动
A charged particle placed in a uniform electric field experiences a constant force F = qE, producing acceleration a = qE/m.
带电粒子在匀强电场中受到恒力F = qE，产生加速度a = qE/m。
If the particle is initially at rest, it moves along the field direction for a positive charge or opposite to it for a negative charge. Its speed increases uniformly.
若粒子初速度为零，则正电荷沿电场方向运动，负电荷沿反方向运动，速度均匀增加。
If the particle enters the field perpendicularly, its trajectory is parabolic. The horizontal velocity remains constant while the vertical acceleration is constant, so the displacement follows y = ½at².
若粒子垂直进入电场，其轨迹为抛物线。水平速度保持不变，垂直方向加速度恒定，位移满足y = ½at²。
This principle is used in cathode-ray tubes, inkjet printers and particle accelerators.
这一原理用于阴极射线管、喷墨打印机和粒子加速器中。
9. Coulomb’s Torsion Balance Experiment | 库仑扭秤实验
The inverse-square law was verified experimentally by Charles Coulomb using a torsion balance. A charged sphere repels another charged sphere mounted on a suspended bar, and the twist angle of the fibre measures the force.
库仑用扭秤实验验证了平方反比定律。带电球排斥悬挂在杆上的另一带电球，纤维的扭转角可测量力的大小。
Coulomb changed the distance between the spheres and measured the corresponding twist angles. He found that the force varies as 1/r², confirmed by the proportionality between the twist angle and the inverse square of the distance.
库仑改变两球之间的距离并测量相应的扭转角。他发现力随1/r²变化，并通过扭转角与距离平方成反比的关系加以证实。
The experiment also showed that the force is directly proportional to the product of the magnitudes of the two charges.
实验还表明，力与两个电荷电荷量的乘积成正比。
10. Comparison with Gravitational Force | 与万有引力的比较
Electrostatic force and gravitational force both obey inverse-square laws, but they differ in several important ways.
静电力和万有引力都遵循平方反比定律，但二者存在若干重要区别。
Electrostatic force can be attractive or repulsive, while gravitational force is always attractive. For example, a proton and an electron attract each other electrically, but two protons repel electrically yet attract gravitationally.
静电力可为吸力或斥力，而万有引力总是引力。例如，质子和电子因电性相互吸引；两个质子因电性相互排斥，但在引力上相互吸引。
Electrostatic force is vastly stronger than gravitational force. For an electron and a proton separated by a typical atomic distance, the electric force is about 10³⁹ times greater than the gravitational force.
静电力远强于万有引力。对于相距典型原子距离的电子和质子，电力大约是引力的10³⁹倍。
Both forces act along the line joining the two objects, and both are inversely proportional to the square of the separation. However, electrostatic force depends on the medium between the charges, whereas gravitational force does not.
两种力都沿两物体连线方向，且都与距离的平方成反比。但静电力受电荷之间介质的影响，而万有引力不受介质影响。
11. Applications of Electrostatic Forces | 静电力的应用
Electrostatic attraction and repulsion are
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