A-Level物理 磁场电场引力场力的比较
一、三种场力：从同一个问题出发 | Three Field Forces: One Question, Three Answers
A-Level 物理中，引力场、电场和磁场是三大核心概念。很多同学在 CIE 考试中分不清这三种力的来源、大小和方向。本文用一条主线对比它们：力由什么产生、大小怎么算、方向指向哪里、能否对物体做功。掌握这套对比框架，无论是选择题还是多步计算题都能快速上手，也为后续的势能、轨道运动和质谱仪等章节打下基础。
In A-Level Physics, gravitational, electric and magnetic fields form the backbone of the forces unit. Many CIE candidates struggle to distinguish where these three forces come from, how their magnitudes are calculated, and which direction they act in. This article compares them along one clear framework: what produces the field, how to calculate the force, which way the force points, and whether the force can do work on the object. Once you hold this comparison in mind, both multiple-choice questions and multi-step calculations become much more manageable, and the same framework carries over to potential energy, orbital motion and the mass spectrometer in later chapters.
二、引力公式 F=GMm/r²：质量之间的万有引力 | Gravitational Force: F = GMm/r²
牛顿万有引力定律指出，两个质点之间的引力与两质量的乘积成正比，与距离的平方成反比，F=GMm/r²。G 是万有引力常量，约为 6.67×10⁻¹¹ N·m²/kg²，数值极小，所以日常物体之间的引力微乎其微。质量永远是正的，因此引力永远是吸引力，这是引力场与电场最根本的区别之一。在地球表面，该定律退化为熟悉的重量公式 W=mg，其中 g≈9.81 N/kg。
Newton's law of universal gravitation states that the force between two point masses is proportional to the product of the masses and inversely proportional to the square of the distance between them. The gravitational constant G is extremely small, about 6.67 × 10⁻¹¹ N m² kg⁻², which is why everyday objects do not attract one another noticeably. Because mass is always positive, the gravitational force is always attractive; it can never push objects apart. This is one of the most fundamental differences between gravity and electricity. Near the Earth's surface the same law reduces to the familiar weight equation W = mg, with g ≈ 9.81 N kg⁻¹, and the direction of the force is always towards the centre of the Earth.
三、库仑定律 F=kQq/r²：电荷之间的静电力 | Coulomb's Law: F = kQq/r²
库仑定律在形式上与万有引力定律惊人地相似：两个点电荷之间的静电力与电荷量乘积成正比，与距离平方成反比，F=kQq/r²，其中 k=1/(4πε₀)≈9.0×10⁹ N·m²/C²。关键区别在于电荷有正负：同号相斥、异号相吸。静电力比同距离的引力强约 10³⁶ 倍，因此在原子尺度上电力完全主导，引力只在行星、恒星这样的大质量天体之间才变得显著。
Coulomb's law has a strikingly similar mathematical form: the force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation. The constant k is about 9.0 × 10⁹ N m² C⁻². The critical difference is that charge comes in two signs: like charges repel while opposite charges attract. The electric force is roughly 10³⁶ times stronger than gravity at the same separation, which is why electric interactions completely dominate inside atoms and molecules, while gravity only becomes significant between very large masses such as planets and stars. Whenever you compare the two equations in an exam, state the common inverse-square form first and then contrast the constants and the signs.
四、磁场力 F=Bqv sinθ：只作用于运动电荷 | Magnetic Force on a Moving Charge: F = Bqv sinθ
磁场力与引力、电场力完全不同：它只作用于运动电荷。把静止电荷放进磁场，它不受任何力。运动电荷所受的洛伦兹力大小为 F=Bqv sinθ，θ 是速度方向与磁场方向的夹角。当速度与磁场平行时 sinθ=0，力为零；当速度垂直于磁场时，力达到最大值 Bqv。正是这一性质，让磁场成为天然的粒子偏转器。
The magnetic force is fundamentally different from gravity and the electric force: it acts only on moving charges. A stationary charge placed in a magnetic field feels no force at all. For a charge moving with speed v at angle θ to the field, the magnitude is F = Bqv sinθ. When the velocity is parallel to the field, sinθ = 0 and the force vanishes; when the velocity is perpendicular to the field, the force reaches its maximum value Bqv. This property makes magnetic fields natural particle deflectors, and it explains why a charged particle moving perpendicular to a uniform field follows a circular path: the magnetic force supplies the centripetal force that continually bends the trajectory.
五、载流导线受力 F=BIL sinθ：从微观到宏观 | Force on a Current-Carrying Conductor: F = BIL sinθ
电流的本质是大量电荷的定向移动，所以载流导线放在磁场中也会受力：F=BIL sinθ，其中 I 是电流，L 是导线在磁场中的有效长度。方向用弗莱明左手定则判断：让磁感线穿入手心，四指指向电流方向，拇指所指就是受力方向。这个电机效应是电动机、扬声器和电流计的工作原理，也是 A-Level 实验题的常客。
Since an electric current is simply a stream of moving charges, a current-carrying conductor placed in a magnetic field also experiences a force. The magnitude is F = BIL sinθ, where I is the current and L is the effective length of wire inside the field. Fleming's left-hand rule gives the direction: hold the thumb, first finger and second finger mutually at right angles, let the first finger point along the field and the second finger along the current, and the thumb shows the direction of the force. This motor effect is the working principle behind electric motors, loudspeakers and moving-coil galvanometers, and it is a favourite context for CIE practical-style questions that ask you to predict the direction of motion of a wire or a coil.
六、力的方向：径向还是垂直 | Direction of the Force: Radial vs Perpendicular
引力和电场力的方向都沿着两物体（或两电荷）的连线，属于径向力，可以直接改变物体的速率。磁场力则始终垂直于速度与磁场构成的平面，只能改变速度的方向，不能直接改变速率。理解了这一点，就能解释为什么带电粒子在匀强磁场中做匀速圆周运动：磁场力时刻提供向心加速度，却不对粒子做功。
Gravitational and electric forces both act along the line joining the two interacting objects; they are radial forces and can directly speed an object up or slow it down. The magnetic force, by contrast, is always perpendicular to both the velocity and the field, so it can change only the direction of motion, never the speed itself. This single fact explains why a charged particle entering a uniform magnetic field at right angles moves in a circle at constant speed: the magnetic force continuously provides the centripetal acceleration while doing no work on the particle. In exam sketches, always label the force arrow at right angles to the velocity, never along it.
七、为什么引力与静电力都是反平方定律 | Why Gravity and Electrostatics Follow the Inverse Square Law
万有引力和库仑力都遵守反平方定律，这不是巧合。想象一个点源向四周均匀发出场线：在距离 r 处，场线分布在一个半径为 r 的球面上，球面面积是 4πr²。距离加倍，球面面积变成四倍，场线密度（即场强）降为原来的四分之一。所以 g=GM/r² 和 E=kQ/r² 中的 r² 来自三维空间的几何特性。磁场没有孤立磁极，磁感线总是闭合的，因此不存在简单的反平方形式的磁场力公式。
The inverse square behaviour of gravity and electrostatics is no coincidence. Imagine a point source emitting field lines uniformly in all directions. At distance r the field lines spread over the surface of a sphere of radius r, whose area is 4πr². Double the distance and the same field lines are spread over four times the area, so the line density, and hence the field strength, falls to one quarter of its original value. This geometric argument is why both g = GM/r² and E = kQ/r² contain r². Magnetic fields, in contrast, do not follow a simple inverse square law from isolated poles, because magnetic monopoles have never been observed and magnetic field lines always form closed loops.
八、场强 g、E 与 B 的定义对比 | Field Strength Defined: g, E and B
场强描述单位受体受到的力。引力场强 g=F/m，单位 N/kg 或 m/s²；电场强度 E=F/q，单位 N/C 或 V/m；磁感应强度 B=F/(qv sinθ)，单位特斯拉 T，也可以写成 N/(A·m)。对比可知：g 和 E 的测试物分别是单位质量和单位电荷，而 B 的测试物必须是运动电荷，这再次体现了磁场力的特殊性。
Field strength measures the force experienced by a unit test object. Gravitational field strength g = F/m has units N kg⁻¹ or m s⁻²; electric field strength E = F/q has units N C⁻¹ or V m⁻¹; magnetic flux density B = F/(qv sinθ) has units tesla (T), equivalent to N A⁻¹ m⁻¹. The test objects reveal the physics: gravity tests a unit mass, electricity tests a unit charge, and magnetism tests a unit charge moving at unit speed. Because B is defined through a moving test charge, the magnetic field can exert forces only on moving charges and currents. Remember that g and E are vectors pointing towards the source of an attractive field, while B points along the field direction defined by the north-seeking pole of a compass.
九、质量与电荷：吸引与排斥的本质 | Mass vs Charge: The Origin of Attraction and Repulsion
为什么引力只有吸引，电力却有吸引和排斥？因为质量只有一种符号，永远是正的；电荷却有正负两种符号。物理学家曾猜想存在磁单极子（单独的 N 极或 S 极），但至今没有发现，所以磁感线总是闭合的。这些符号特性决定了宇宙中的运动形态：引力让行星绕太阳运转，电力维持原子与分子的稳定，磁场则让带电粒子在加速器和极光中画圆。
Why is gravity purely attractive while electricity can both attract and repel? Because mass has only one sign, always positive, whereas charge comes in two signs. Physicists have long speculated about magnetic monopoles, isolated north or south poles, but none has ever been observed, which is why magnetic field lines always form closed loops. These sign properties shape the observable universe: gravity binds planets to stars, electric forces hold atoms and molecules together, and magnetic forces steer charged particles into circular paths in accelerators and in the auroras near the Earth's poles. When a question asks why gravity is always attractive, the examiner wants the one-line answer: mass is always positive, so the product of masses is always positive and the force always points towards the source.
十、为什么磁场力永远不做功 | Why the Magnetic Force Never Does Work
功的定义是 W=Fs cosθ，θ 是力与位移的夹角。磁场力始终垂直于速度，也就垂直于位移，cos90°=0，因此 W=0。这意味着磁场力不能改变物体的动能，只能改变运动方向。相反，引力与电场力可以做正功或负功，把势能转化为动能。这个对比是 A-Level 简答题的高频考点。
Work is defined as W = Fs cosθ, where θ is the angle between the force and the displacement. Since the magnetic force is always perpendicular to the velocity, it is also perpendicular to the displacement, cos 90° = 0, and the work done is zero. The magnetic force therefore cannot change the kinetic energy of a particle; it only redirects the motion. Gravitational and electric forces, by contrast, can do positive or negative work, converting potential energy into kinetic energy and back again. This contrast is a favourite short-answer question: examiners expect you to state that the magnetic force is always perpendicular to the velocity, so the speed and kinetic energy of a charged particle in a pure magnetic field remain constant, and then to link this to circular motion rather than speeding up or slowing down.
十一、电场力与磁场力对速度的依赖 | Velocity Dependence: Electric vs Magnetic Force
F=qE 与速度无关：电荷无论静止还是运动，受到的电场力都一样；F=Bqv 则与速度成正比。这个差异催生了经典实验装置：速度选择器中，电场力与磁场力平衡，qvB=qE，只有速度 v=E/B 的粒子能直线通过。质谱仪正是利用这个原理筛选不同质荷比的离子，这也是 CIE 计算题的经典背景。
The electric force F = qE does not depend on velocity; a charge feels the same force whether it is stationary or moving. The magnetic force F = Bqv, however, is proportional to speed. This contrast powers a classic experimental device: the velocity selector. When an electric field and a magnetic field are arranged at right angles, a charged particle experiences qE from the electric field and qvB from the magnetic field. Only particles with v = E/B travel in a straight line, because for those particles the two forces exactly cancel. Mass spectrometers and cyclotrons rely on this velocity filtering and on the circular motion produced by magnetic fields to separate ions by their mass-to-charge ratio. In calculations, set the two force expressions equal and solve for v, then check the units of E and B carefully.
十二、A-Level 常考题型与易错点 | Common Exam Questions and Common Mistakes
CIE 试卷中这个主题常见四种考法：直接套公式比较三种力的大小；画出带电粒子在磁场中的轨迹；解释磁场力为什么不做功；计算速度选择器中的 v=E/B。高频易错点包括：忘记 sinθ；把引力画成斥力；认为静止电荷受磁场力；把特斯拉写成 N/C；混淆引力势能与电势能的符号。考前把这些点逐个过一遍，这类计算题基本可以拿满分。
In CIE papers this topic appears in four typical ways: direct calculation comparing the magnitudes of the three forces; sketching the path of a charged particle in a magnetic field; explaining why the magnetic force does no work; and calculating the pass-through speed in a velocity selector. The most common mistakes are forgetting the sinθ factor, drawing gravity as a repulsive force, claiming that a stationary charge experiences a magnetic force, writing the tesla as N/C, and confusing the sign conventions of gravitational and electric potential energy. If you work through each of these pitfalls before the exam, the calculation questions in this area are among the easiest full marks on the paper: write down the formula, substitute with consistent SI units, and state the direction of the force explicitly.
需要专业A-Level辅导？
16621398022
同微信 | 免费咨询课程规划
访问 aleveler.com 了解更多
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图