📚 Attraction and Repulsion in Electric and Magnetic Fields | 电场与磁场中的吸引与排斥
Attraction and repulsion are fundamental ideas in A-Level Physics. In electricity and magnetism, forces can pull objects together or push them apart, depending on the signs of charges, the orientation of magnetic poles, or the directions of currents. Understanding these interactions is key to explaining static electricity, electric fields, motors, charged particle deflection and electromagnetic induction.
吸引与排斥是 A-Level 物理中的基本概念。在电学和磁学中，力可以把物体拉近或推开，具体取决于电荷的符号、磁极的取向或电流的方向。理解这些相互作用，是解释静电、电场、电动机、带电粒子偏转和电磁感应等现象的关键。
1. The Big Picture: Forces That Pull and Push | 总体图景：拉近与推开的力
In the CIE A-Level syllabus, attraction and repulsion appear mainly in electrostatics and magnetism. Electric forces act between charges, while magnetic forces act between magnetic poles, between magnets and currents, and between current-carrying conductors. Gravitational force is different because it is always attractive; there is no gravitational repulsion.
在 CIE A-Level 大纲中，吸引与排斥主要出现在静电学和磁学中。电力作用在电荷之间，而磁力作用在磁极之间、磁体与电流之间以及载流导体之间。万有引力则不同，因为它总是吸引力，不存在引力排斥。
When two objects repel, the field lines or force directions point away from each other. When they attract, the force directions point towards each other. Recognising whether a given configuration attracts or repels is often tested by asking you to predict motion, draw field lines, or use Fleming’s left-hand rule.
当两个物体相互排斥时，电场线或力的方向彼此远离；当它们相互吸引时，力的方向彼此指向。判断某种结构是吸引还是排斥，经常出现在预测运动、画电场线或使用弗莱明左手定则的考题中。
2. Electric Charge and Coulomb’s Law | 电荷与库仑定律
Electric charge exists in two types: positive and negative. The basic rule is simple: like charges repel, and unlike charges attract. A proton carries positive charge, an electron carries negative charge, and the magnitude of the elementary charge is e = 1.60 × 10⁻¹⁹ C.
电荷有两种：正电荷和负电荷。基本规则很简单：同性电荷相斥，异性电荷相吸。质子带正电荷，电子带负电荷，基本电荷的大小为 e = 1.60 × 10⁻¹⁹ C。
Coulomb’s law gives the size of the electrostatic force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of their separation. The direction is attractive for opposite signs and repulsive for the same signs.
库仑定律给出了两个点电荷之间静电力的大小。力与电荷的乘积成正比，与它们距离的平方成反比。方向为异性电荷相吸，同性电荷相斥。
F = Q₁Q₂ / (4πε₀r²)
Here ε₀ is the permittivity of free space, ε₀ = 8.85 × 10⁻¹² F m⁻¹. The constant can also be written as k = 1 / (4πε₀) ≈ 8.99 × 10⁹ N m² C⁻².
其中 ε₀ 是真空介电常数，ε₀ = 8.85 × 10⁻¹² F m⁻¹。这个常量也可以写成 k = 1 / (4πε₀) ≈ 8.99 × 10⁹ N m² C⁻²。
Because Coulomb’s law is an inverse-square law, doubling the distance reduces the force to one quarter. The force is very large for charges of about 1 C, but everyday static charges are usually in the microcoulomb or nanocoulomb range.
由于库仑定律是平方反比定律，距离加倍会使力减小到原来的四分之一。对于约 1 C 的电荷，力非常大，但日常静电电荷通常在微库仑或纳库仑范围内。
3. Electric Fields: Lines of Force and Direction | 电场：力线与方向
An electric field is a region where a charge experiences a force. Electric field strength is defined as the force per unit positive charge. The direction of the electric field is the direction of the force on a small positive test charge.
电场是电荷会受到力的区域。电场强度定义为单位正电荷所受的力。电场的方向就是作用在小正检验电荷上的力的方向。
E = F / q
For a point charge, the field strength at a distance r is given by E = Q / (4πε₀r²). The field is radial: it points away from a positive charge and towards a negative charge. This directly shows why a positive and a negative charge attract: each charge lies in the field of the other and experiences a force towards the source charge.
对于点电荷，距离 r 处的电场强度为 E = Q / (4πε₀r²)。该电场是辐射状的：正电荷的电场向外指，负电荷的电场向内指。这直接说明了为什么正负电荷相互吸引：每个电荷都处在另一个电荷的电场中，并受到指向源电荷的力。
In a uniform electric field between two parallel charged plates, the field strength is constant and can be calculated using E = V / d, where V is the potential difference and d is the plate separation. A positive charge accelerates in the direction of the field, while a negative charge accelerates opposite to the field direction.
在两块带电平行板之间的匀强电场中，电场强度恒定，可以用 E = V / d 计算，其中 V 是电势差，d 是板间距离。正电荷沿电场方向加速，负电荷沿电场反方向加速。
4. Charging by Friction and Induction | 摩擦起电与感应起电
Everyday attraction and repulsion can be demonstrated with insulating rods. When a polythene rod is rubbed with wool, electrons transfer from the wool to the rod, giving the polythene a negative charge. When an acetate rod is rubbed with wool, electrons transfer from the rod to the wool, leaving the acetate positively charged.
日常的吸引与排斥可以用绝缘棒来演示。用羊毛摩擦聚乙烯棒时，电子从羊毛转移到聚乙烯棒上，使聚乙烯带负电。用羊毛摩擦醋酸纤维棒时，电子从醋酸纤维棒转移到羊毛上，使醋酸纤维棒带正电。
Two charged polythene rods repel each other because they carry the same sign of charge. A charged polythene rod and a charged acetate rod attract because their charges are opposite. A charged rod can also attract small neutral pieces of paper by induction: the rod repels like charges within the paper and attracts the opposite charges closer to its surface.
两根带电的聚乙烯棒相互排斥，因为它们带同种电荷。带电的聚乙烯棒和带电的醋酸纤维棒相互吸引，因为它们的电荷相反。带电棒还可以通过感应吸引轻小的中性纸片：棒排斥纸片中的同种电荷，并吸引靠近棒表面的异种电荷。
A gold-leaf electroscope can be used to test charge. When a charged object touches the metal cap, charge spreads to the gold leaf and the stem. Since both receive the same sign of charge, the leaf repels the stem and rises. The larger the charge, the greater the repulsion.
金箔验电器可以用来检验电荷。当带电物体接触金属帽时，电荷会传到金箔和金属杆上。由于金箔和金属杆带同种电荷，金箔与金属杆相互排斥而张开。电荷越大，排斥力越大。
5. Magnetic Poles: Like Poles Repel, Unlike Poles Attract | 磁极：同名相斥，异名相吸
Magnets have two poles: north and south. The basic law of magnetic poles is that like poles repel and unlike poles attract. A north pole repels another north pole, a south pole repels another south pole, and a north pole attracts a south pole.
磁体有两个磁极：北极和南极。磁极的基本定律是同名磁极相斥，异名磁极相吸。北极排斥另一个北极，南极排斥另一个南极，北极吸引南极。
Isolated magnetic poles, called magnetic monopoles, have never been observed. If you cut a bar magnet in half, you do not get a separate north pole and a separate south pole. Instead, each half becomes a complete magnet with its own north and south poles.
孤立的磁极，即磁单极子，从未被观测到。如果把条形磁铁切成两半，你不会得到单独的北极和单独的南极。相反，每一半都会变成具有自己的北极和南极的完整磁体。
The Earth behaves like a large magnet. The geographic north pole is actually close to a magnetic south pole, which is why the north pole of a compass needle points towards geographic north. The compass needle itself is a small magnet, so it experiences attraction and repulsion in the Earth’s magnetic field.
地球就像一个大磁体。地理北极实际上靠近磁南极，这就是为什么指南针的北极指向地理北方。指南针本身就是一个小的磁体，因此它会在地球磁场中受到吸引和排斥。
6. Magnetic Fields and Field Lines | 磁场与磁感线
A magnetic field is a region where a magnetic material or a moving charge experiences a force. Magnetic field lines are drawn from the north pole to the south pole outside a magnet, and they continue inside the magnet from south to north, forming closed loops.
磁场是磁性材料或运动电荷会受到力的区域。磁感线在磁体外部从北极画到南极，并在磁体内部从南极到北极，形成闭合回路。
The direction of a magnetic field at a point is the direction in which a small north pole would point. Field lines never cross. The closer the lines are spaced, the stronger the magnetic field. A uniform magnetic field is represented by equally spaced parallel lines.
磁场中某点的方向就是小北极在该点所指的方向。磁感线永不相交。磁感线越密，磁场越强。匀强磁场用等间距的平行线表示。
When two magnets are brought together, their fields combine. Between unlike poles, the field lines link from north to south and the magnets attract. Between like poles, the field lines bend away from each other, creating a neutral point where the resultant field is zero, and the magnets repel.
当两个磁体靠近时，它们的磁场会叠加。在异名磁极之间，磁感线从北极连到南极，磁体相互吸引。在同名磁极之间，磁感线彼此弯曲远离，产生一个合磁场为零的中性点，磁体相互排斥。
7. Magnetic Force on a Current-Carrying Conductor | 磁场对载流导体的力
A current-carrying conductor placed in a magnetic field experiences a force, provided the current is not parallel to the field. The size of the force is given by F = BIL sin θ, where B is the magnetic flux density, I is the current, L is the length of conductor in the field, and θ is the angle between the current and the magnetic field.
放在磁场中的载流导体会受到力的作用，只要电流不与磁场平行。力的大小由 F = BIL sin θ 给出，其中 B 是磁通密度，I 是电流，L 是导体在磁场中的长度，θ 是电流与磁场之间的夹角。
F = BIL sin θ
The direction of the force is given by Fleming’s left-hand rule. Point the first finger in the direction of the magnetic field, the second finger in the direction of conventional current, then the thumb gives the direction of the force. Reversing either the current or the field reverses the force, which can change attraction into repulsion in devices such as motors and loudspeakers.
力的方向由弗莱明左手定则确定。将食指指向磁场方向，中指指向常规电流方向，拇指所指的方向就是力的方向。反转电流或磁场方向都会反转力的方向，这可以在电动机和扬声器等装置中把吸引变为排斥。
The interaction between the conductor’s own magnetic field and the external field is another way to understand the force. On one side of the wire the fields add, and on the other side they oppose. The wire is pushed from the stronger-field region towards the weaker-field region, producing a repulsion or attraction effect relative to the external magnet.
导体自身磁场与外加磁场的相互作用是理解该力的另一种方式。在导线一侧磁场增强，另一侧磁场减弱。导线从磁场较强的区域被推向磁场较弱的区域，从而产生相对于外部磁体的排斥或吸引效果。
8. Force on a Moving Charge | 磁场对运动电荷的力
A charged particle moving through a magnetic field also experiences a magnetic force. For a particle with charge q moving at speed v at angle θ to the magnetic field, the force is F = qvB sin θ. The force is zero when the particle moves parallel to the field.
带电粒子穿过磁场时也会受到磁力。对于电荷为 q、速度为 v、速度方向与磁场夹角为 θ 的粒子，力为 F = qvB sin θ。当粒子沿磁场方向运动时，力为零。
F = qvB sin θ
The direction of the force is perpendicular to both the velocity and the magnetic field. For a positive charge, Fleming’s left-hand rule uses the conventional current direction, which is the direction of motion. For a negative charge, the force is opposite to that given for a positive charge moving in the same direction.
力的方向同时垂直于速度和磁场。对于正电荷，弗莱明左手定则使用常规电流方向，即正电荷的运动方向。对于负电荷，力的方向与正电荷沿同一方向运动时相反。
If the velocity is perpendicular to a uniform magnetic field, the particle moves in a circle because the magnetic force is always perpendicular to the velocity and acts as a centripetal force. The radius of the circular path is r = mv / (Bq). Positive and negative charges curve in opposite directions, showing a type of directional attraction or repulsion relative to the field source.
如果速度垂直于匀强磁场，粒子将做圆周运动，因为磁力始终垂直于速度并充当向心力。圆周路径的半径为 r = mv / (Bq)。正电荷和负电荷向相反方向偏转，这体现了相对于场源的一种方向性吸引或排斥。
9. Attraction and Repulsion Between Parallel Currents | 平行电流之间的吸引与排斥
Two parallel current-carrying wires exert magnetic forces on each other. If the currents flow in the same direction, the wires attract. If the currents flow in opposite directions, the wires repel. This is a direct example of magnetic attraction and repulsion caused by moving charges.
两根平行的载流导线彼此施加磁力。如果电流方向相同，导线相互吸引；如果电流方向相反，导线相互排斥。这是由运动电荷引起的磁吸引和磁排斥的直接例子。
Each wire produces a magnetic field around itself. The second wire sits in that field and carries a current, so it experiences a force F = BIL. Using the right-hand grip rule and Fleming’s left-hand rule together shows that the force is attractive for parallel currents and repulsive for anti-parallel currents.
每根导线都在其周围产生磁场。另一根导线处于该磁场中并载有电流，因此会受到力 F = BIL。同时使用右手螺旋定则和弗莱明左手定则可以表明，电流同向时力为吸引力，电流反向时力为排斥力。
The force per unit length between two long straight parallel conductors separated by distance r is:
F / L = μ₀ I₁ I₂ / (2πr)
Here μ₀ is the permeability of free space, μ₀ = 4π × 10⁻⁷ H m⁻¹. This equation is part of the CIE A-Level specification and explains why large currents in parallel bus bars can produce noticeable mechanical forces.
其中 μ₀ 是真空磁导率，μ₀ = 4π × 10⁻⁷ H m⁻¹。该公式属于 CIE A-Level 考试范围，解释了为什么平行母线中的大电流会产生明显的机械力。
10. Electromagnetic Induction and Lenz’s Law | 电磁感应与楞次定律
Electromagnetic induction also shows attraction and repulsion effects. When the magnetic flux linking a circuit changes, an emf is induced. The direction of the induced current is such that it opposes the change producing it. This is Lenz’s law.
电磁感应也表现出吸引与排斥效应。当穿过电路的磁通量发生变化时，会感应出电动势。感应电流的方向总是阻碍引起它的变化。这就是楞次定律。
EMF = -N ΔΦ / Δt
The negative sign in Faraday’s equation represents Lenz’s law. If a north pole of a magnet approaches a coil, the coil induces a current that creates a north pole facing the incoming magnet, so the magnet is repelled. If the magnet is pulled away, the coil induces a current that creates a south pole facing the magnet, so the magnet is attracted back.
法拉第方程中的负号代表楞次定律。如果磁铁的北极靠近线圈，线圈中感应出的电流会产生一个面对来磁的北极，因此磁铁被排斥。如果磁铁被拉远，线圈会感应出电流，产生一个面对磁铁的南极，因此磁铁被吸引回来。
This is why a magnet falling through a conducting pipe falls slower than in air. Induced currents in the pipe produce magnetic fields that oppose the motion, creating drag forces that can be described as repulsion from the approaching pole and attraction to the receding pole.
这就是为什么磁铁在导电管中下落比在空气中慢。管中感应出的电流产生阻碍运动的磁场，形成阻力，可以描述为来自靠近磁极的排斥力和来自远离磁极的吸引力。
11. Comparing Electric, Magnetic and Gravitational Interactions | 比较电、磁和引力相互作用
It is useful to compare the three field-based interactions in A-Level Physics. Gravitational forces always attract, electric forces can attract or repel, and magnetic forces can attract or repel depending on pole orientation or current direction. All three obey inverse-square laws in their point-source forms, although the magnetic force between poles is more complex because isolated poles do not exist.
比较 A-Level 物理中三种基于场的相互作用很有帮助。万有引力总是吸引，电力可以吸引或排斥，磁力根据磁极方向或电流方向可以吸引或排斥。三者在点源形式下都遵循平方反比定律，不过磁极之间的力更为复杂，因为孤立的磁极并不存在。
| Interaction 相互作用 | Attract or repel? 吸引还是排斥？ | Typical formula 典型公式 | Relative strength 相对强度 |
|---|---|---|---|
| Gravitational 万有引力 | Attraction only 仅吸引 | F = G m₁ m₂ / r² | Weakest 最弱 |
| Electrostatic 静电 | Attract or repel 吸引或排斥 | F = Q₁ Q₂ / (4πε₀r²) | Much stronger 强得多 |
| Magnetic 磁力 | Attract or repel 吸引或排斥 | F = BIL sin θ or qvB sin θ | Strong 强 |
Despite their differences, electric and magnetic interactions are unified in the theory of electromagnetism. A magnetic field is produced by moving charges, and a changing magnetic field produces an electric field. This connection is central to generators, transformers and electromagnetic waves.
尽管存在差异，电与磁相互作用在电磁学理论中是统一的。磁场由运动的电荷产生，变化的磁场会产生电场。这种联系对于发电机、变压器和电磁波至关重要。
12. Exam Tips and Common Misconceptions | 考试技巧与常见误区
A common mistake is to say that field lines show the path a charged particle would follow. Field lines show the direction of force on a positive test charge, not the trajectory. A charged particle entering a uniform electric field follows a parabolic path, while in a perpendicular magnetic field it follows a circular path.
一个常见错误是认为电场线表示带电粒子运动的轨迹。电场线表示正检验电荷的受力方向，而不是运动轨迹。进入匀强电场的带电粒子沿抛物线运动，而在垂直磁场中则沿圆周运动。
Another misconception is to forget the sign of the charge when using Fleming’s left-hand rule. The rule uses conventional current, which is the direction of flow of positive charge. For an electron beam, the force direction is opposite to that predicted for positive current in the same direction as the beam.
另一个误区是在使用弗莱明左手定则时忘记电荷的符号。该定则使用常规电流，即正电荷流动的方向。对于电子束，力的方向与正电荷沿电子束方向运动时的预测方向相反。
Students also confuse the right-hand grip rule with Fleming’s left-hand rule. The grip rule gives the direction of the magnetic field around a current, while the left-hand rule gives the force on a current in an external magnetic field. Practising questions that require predicting attraction or repulsion between charges, magnets, and currents will help you avoid these errors.
学生还容易混淆右手螺旋定则和弗莱明左手定则。右手螺旋定则给出电流周围的磁场方向，而左手定则给出电流在外磁场中的受力方向。多练习判断电荷、磁体和电流之间吸引或排斥的题目，
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