📚 Comparing Forces in Magnetic, Electric and Gravitational Fields | 磁场、电场与引力场中的力比较
In A-Level Physics, magnetic, electric and gravitational fields are three fundamental ways in which objects can exert forces without direct contact. Although they share some mathematical similarities, their origins, directions, work done and effects on matter are very different. This article compares the forces in these three fields, section by section, and highlights what CIE and Edexcel exam questions usually test.
在 A-Level 物理中，磁场、电场和引力场是物体不直接接触却能产生力的三种基本方式。虽然它们在数学形式上有一些相似之处，但力的来源、方向、做功方式以及对物质的作用差别很大。本文逐节比较这三种场中的力，并突出 CIE 与 Edexcel 考试常见的考查点。
1. What a Field Is | 什么是场
A field is a region of space in which a suitable object experiences a non-contact force. Gravitational fields act on mass, electric fields act on electric charge, and magnetic fields act on moving charges and on magnetic materials such as iron, cobalt and nickel.
场是空间中的一个区域，其中合适的物体会受到非接触力。引力场作用于质量，电场作用于电荷，磁场作用于运动电荷和铁、钴、镍等磁性材料。
The essential idea is that every field has its own source property. Mass is the gravitational source, electric charge is the electric source, and magnetic effects require moving charge or a permanent magnet. Magnetic monopoles have not been observed, so there is no magnetic equivalent of a single isolated charge.
核心思路是：每种场都有自己的源属性。质量是引力场的源，电荷是电场的源，而磁效应需要运动电荷或永磁体。磁单极子至今未被观察到，因此不存在与孤立电荷对应的磁荷。
A second crucial difference is that gravitational and electric fields can be produced by completely static sources, whereas a magnetic field requires something to be moving. A stationary charge produces no magnetic field and feels no magnetic force, no matter how strong the nearby magnetic flux density is.
第二个关键区别是：引力场和电场可以由完全静止的源产生，而磁场需要某种运动。静止电荷不产生磁场，也不受磁力，无论附近的磁感应强度有多大。
2. Field Lines and Their Conventions | 场线及其约定
Field lines are used to represent fields. The direction of a field line shows the direction of the force that would act on a small positive test mass, a small positive test charge, or a north magnetic pole. The spacing of the lines indicates the strength of the field: closely spaced lines mean a strong field.
场线用来表示场。场线方向表示作用在一个小的正试探质量、正试探电荷或 N 磁极上的力的方向。场线的疏密表示场的强弱：线越密表示场越强。
Gravitational field lines point radially inwards towards the mass, because gravity is always attractive. Electric field lines point away from positive charges and towards negative charges. Magnetic field lines outside a magnet run from the north pole to the south pole, but inside the magnet they continue from south to north, so they always form closed loops.
引力场线沿径向指向质量内部，因为引力总是吸引的。电场线从正电荷指向外、指向负电荷。磁体外部磁感线从 N 极到 S 极，但磁体内部从 S 极回到 N 极，因此总是形成闭合回路。
Because field lines can never cross, and because the closed-loop nature of magnetic field lines reflects the absence of monopoles, this single convention already tells you that the three fields are not simply three copies of each other.
由于场线永不相交，且磁感线的闭合特性正反映了磁单极子的缺失，仅凭这一约定就能说明这三种场并非彼此的简单翻版。
3. Gravitational Force: Newton's Law of Gravitation | 引力场中的力
A gravitational field exerts a force on any mass. Near the Earth's surface the field is approximately uniform, so the weight of a mass m is given by:
引力场对任何质量施加力。在地球表面附近，引力场近似均匀，因此质量为 m 的物体所受重力为：
F = m g
For two point masses, Newton's law of gravitation gives an attractive force along the line joining them:
对于两个点质量，牛顿万有引力定律给出沿两质量连线方向的吸引力：
F = G m₁ m₂ / r²
e distance between the centres of the masses. Gravitational fields are uniform only far from the source compared with the size of the region considered; the Earth's field decreases from about 9.81 N kg⁻¹ at the surface.
其中 G = 6.67 × 10⁻¹¹ N m² kg⁻²，r 是两质量中心之间的距离。只有当所考虑区域的尺度远小于到源的距离时，引力场才可视为均匀场；地球的场强从表面约 9.81 N kg⁻¹ 向外递减。
The field strength of a point mass is found by dividing the force by the test mass:
点质量的场强可由力除以试探质量得到：
g = F / m = G M / r²
Note that g is a vector quantity, always directed towards the source mass, and it does not depend on the mass placed in the field. This is why all objects fall with the same acceleration in a vacuum.
注意 g 是矢量，方向始终指向源质量，且与被放入场中的物体质量无关。这正是所有物体在真空中以相同加速度下落的原因。
4. Electric Force: Coulomb's Law | 电场中的力
An electric field exerts a force on any charge. For two point charges in a vacuum or in air, Coulomb's law gives:
电场对任何电荷施加力。对于真空或空气中的两个点电荷，库仑定律给出：
F = k Q₁ Q₂ / r² = Q₁ Q₂ / (4 π ε₀ r²)
ve the same sign the force is repulsive; if they have opposite signs the force is attractive.
其中 k = 1 / (4 π ε₀) ≈ 8.99 × 10⁹ N m² C⁻²，ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹。若 Q₁ 与 Q₂ 同号，力为排斥力；若异号，力为吸引力。
Electric field strength is the force per unit positive charge, and for a radial field around a point charge Q:
电场强度是单位正电荷所受的力，对于点电荷 Q 周围的径向场：
E = F / Q = k Q / r²
Inside a uniform electric field between two parallel plates separated by distance d, the field strength is:
在相距 d 的两平行板之间的匀强电场中，场强为：
E = V / d
s the standard starting point for projectile-style problems involving charged particles between plates.
该区域中电荷 q 所受的电场力就是 F = qE = qV / d，这是处理带电粒子在两板间类平抛运动问题的标准出发点。
5. Magnetic Force on a Moving Charge and on a Current | 运动电荷与电流所受的磁力
A magnetic field exerts a force only on a moving charge or on a current-carrying conductor. For a charge q moving with speed v at an angle θ to the magnetic flux density B:
磁场只对运动电荷或载流导体施加力。对于以速率 v 运动、与磁感应强度 B 成 θ 角的电荷 q：
F = B q v sin θ
For a straight wire of length L carrying current I at an angle θ to B:
对于长为 L、载电流 I、与 B 成 θ 角的直导线：
F = B I L sin θ
80°, that is when the velocity or the current is parallel to the field, the magnetic force is exactly zero.
由此可立即得到两个重要的特殊情况。当 θ = 90° 时力最大，F = Bqv 或 F = BIL。当 θ = 0° 或 180°，即速度或电流与磁场平行时，磁力恰好为零。
The direction of the magnetic force is given by Fleming's left-hand rule: the first finger points along the field, the second finger along the conventional current or velocity of positive charge, and the thumb gives the force. The force is always perpendicular to both B and v, so it does no work on a point charge.
磁力方向由弗莱明左手定则给出：食指指向磁场方向，中指指向常规电流或正电荷运动方向，拇指指向力的方向。该力始终同时垂直于 B 和 v，因此对点电荷不做功。
6. Similarities: Inverse-Square Laws and Mathematical Structure | 相似之处：平方反比律与数学结构
Newton's law of gravitation and Coulomb's law have the same mathematical form. Both fall off as the inverse square of separation, both give a central force along the line joining the two objects, and both satisfy Newton's third law, so the two forces are always equal in magnitude and opposite in direction.
牛顿万有引力定律与库仑定律的数学形式相同。两者都按距离的平方反比衰减，都给出沿两物体连线方向的中心力，且都满足牛顿第三定律，因此两力总是大小相等、方向相反。
Both fields can be described using field strength, potential and potential energy, and both lead to uniform-field approximations that make simple problems solvable with constant-acceleration equations.
两种场都可以用场强、势和势能来描述，也都可以在匀强场近似下用恒定加速度公式解决简单问题。
Another shared feature is that in a radial field the potential energy and potential take simple forms:
另一个共同点是，在径向场中势能与势具有简洁形式：
U = − G M m / r V = − G M / r
U = k Q₁ Q₂ / r V = k Q / r
The minus signs in the gravitational expressions show that the zero of potential energy is taken at infinity and that the force is attractive, whereas the electric expressions carry the signs of the charges themselves.
引力表达式中的负号表明势能零点取在无穷远处，且力为吸引力；而电学表达式中的符号则来自电荷本身的正负。
7. Differences: Attraction, Repulsion and Relative Strength | 差异：吸引、排斥与相对强度
Gravity is only ever attractive, because there is no negative mass. The electric force can be attractive or repulsive, and the magnetic force can be attractive or repulsive depending on the relative directions of the currents. This single difference changes the whole geometry of the field lines and of the resulting motion.
引力只能是吸引的，因为不存在负质量。电场力可以是吸引的也可以是排斥的，磁力则取决于电流的相对方向而可吸可斥。仅这一差异就改变了场线以及由此产生的运动的整体几何形态。
The electric force between two charged particles is enormously stronger than the gravitational force between them. For two protons separated by the same distance, the ratio of the electrostatic repulsion to the gravitational attraction is of the order of 10³⁶.
两个带电粒子之间的电场力远大于它们之间的引力。对于相距同样距离的两个质子，静电斥力与引力之比约为 10³⁶ 量级。
This is why gravity dominates on astronomical scales: large bodies are almost exactly electrically neutral, so the electric forces cancel, while mass always adds up. In the laboratory, however, electric and magnetic forces dominate every practical experiment.
这就是引力在天文尺度上占主导的原因：大尺度天体几乎完全电中性，电场力相互抵消，而质量总是累加的。但在实验室中，电场力与磁力主导着每一个实际实验。
8. Work Done and the Conservative Nature of the Fields | 做功与场的保守性
Gravitational and electrostatic forces are conservative: the work done in moving an object between two points depends only on the end points, not on the path taken. This is why both fields can be described by a scalar potential.
引力与静电力是保守力：把物体从一点移到另一点所做的功只取决于始末位置，与路径无关。这正是两种场都能用标量势来描述的原因。
The magnetic force behaves very differently. Because the force on a moving charge is always perpendicular to the velocity, the magnetic force does no work at all. The kinetic energy of a charged particle moving in a pure magnetic field is constant; only its direction of motion changes.
磁力的表现则完全不同。由于运动电荷所受的力始终垂直于速度，磁力完全不做功。在纯磁场中运动的带电粒子动能保持不变，改变的只是运动方向。
This contrast explains a classic exam point: a charged particle in a uniform magnetic field moves in a circle at constant speed, while a charge accelerated through a potential difference in an electric field gains kinetic energy according to:
这一对比解释了一个经典考点：带电粒子在匀强磁场中做匀速圆周运动，而电荷在电场中通过电势差被加速时，其动能增加满足：
q V = ½ m v²
9. Field Strength Compared: g, E and B | 场强比较：g、E 与 B
Each field has its own definition of field strength, and these definitions must be memorised precisely because they are frequently examined as definitions rather than calculations.
每种场都有自己的场强定义，这些定义必须准确记忆，因为考试常以定义题而非计算题的形式考查。
- he force per unit mass, g = F / m, unit N kg⁻¹, a vector pointing towards the source mass.
- rge, E = F / Q, unit N C⁻¹ or V m⁻¹, a vector determined by the sign of the source charge.
- placed at right angles to the field, B = F / (I L), unit tesla, T, with 1 T = 1 N A⁻¹ m⁻¹.
- 引力场强度：单位质量所受的力，g = F / m，单位 N kg⁻¹，是矢量，方向指向源质量。
- 电场强度：单位正电荷所受的力，E = F / Q，单位 N C⁻¹ 或 V m⁻¹，是矢量，方向由源电荷的正负决定。
- 磁感应强度：垂直于磁场的导体单位电流、单位长度所受的力，B = F / (I L)，单位特斯拉 T，1 T = 1 N A⁻¹ m⁻¹。
Notice that g and E are defined by dividing a force by the source-independent property of the test object, whereas B must be defined with the conductor perpendicular to the field, because otherwise the geometry introduces a sin θ factor.
注意 g 与 E 都是把力除以试探物体与源无关的属性，而 B 的定义必须要求导体垂直于磁场，否则几何关系会引入 sin θ 因子。
10. Circular Motion and Orbits in the Three Fields | 三种场中的圆周运动与轨道
In a gravitational field, a satellite in circular orbit has the gravitational force providing the centripetal force:
在引力场中，做圆周运动的卫星由引力提供向心力：
G M m / r² = m v² / r → v = √G M / r
T² = 4 π² r³ / (G M)
The last expression is Kepler's third law. In a magnetic field, the same idea gives the radius of the circular path of a charged particle moving perpendicular to B:
最后一式即开普勒第三定律。在磁场中，同样的思路给出垂直于 B 运动的带电粒子的圆周半径：
B q v = m v² / r → r = m v / (B q)
T = 2 π m / (B q)
A striking result is that the time period of the circular motion in a magnetic field does not depend on the speed. This is the principle behind the cyclotron. An electric field, by contrast, drives linear acceleration when the charge moves along the field, and projectile-like parabolic motion when it moves across a uniform field.
一个引人注目的结果是：磁场中圆周运动的周期与速率无关，这正是回旋加速器的原理。相比之下，电场在电荷沿场方向运动时产生直线加速，而在电荷横穿匀强电场时产生类平抛的抛物线运动。
11. Summary Comparison Table | 综合对比表
The table below collects the main points of comparison into a single reference that is useful for last-minute revision.
下表把主要的比较要点集中成一份便于考前快速复习的参考。
| Feature | 特征 | Gravitational | 引力场 | Electric | 电场 | Magnetic | 磁场 |
|---|---|---|---|
| Source | 源 | Mass | Charge | Moving charge or magnet |
| Acts on | 作用于 | Any mass | Any charge | Moving charge, current |
| Force law | 力定律 | F = G m₁ m₂ / r² | F = k Q₁ Q₂ / r² | F = B q v sin θ |
| Direction | 方向 | Always attractive | Attractive or repulsive | Perpendicular to B and v |
| Field lines | 场线 | Radially inward | From + to − | Closed loops |
| Work done on charge | 做功 | Conservative | Conservative | Zero on a moving charge |
Reading the table row by row is a fast way to check that you can state both a similarity and a difference for every pair of fields, which is exactly what comparison questions require.
逐行阅读该表，可以快速检验你是否能对任意两种场都说出一处相同点与一处不同点，而这正是比较型题目所要求的。
12. Exam Technique and Common Traps | 考试技巧与常见易错点
Most lost marks in this topic come from a small number of repeated errors rather than from a lack of understanding. Checking these points before the exam is worthwhile.
本专题的大部分失分来自少数反复出现的错误，而非理解不足。考前检查以下几点很有价值。
- Do not confuse field strength with force: g and E are per unit mass or charge, while F depends on the test object as well as the source.
- Remember that the magnetic force is zero when the velocity or current is parallel to B; sin θ, not cos θ, is used.
- Use r as the distance between centres for spheres and point masses or charges, not the distance to the surface.
- Keep the signs of charges when substituting into Coulomb's law and into potential formulae; a negative answer means attraction.
- State the direction of a vector answer explicitly, since many mark schemes award a mark for direction alone.
- Quote the correct units: N kg⁻¹ for g, N C⁻¹ or V m⁻¹ for E, and tesla for B.
- 不要把场强与力混为一谈：g 与 E 是单位质量或单位电荷的量，而 F 同时取决于源与试探物体。
- 记住当速度或电流与 B 平行时磁力为零；公式用的是 sin θ 而不是 cos θ。
- 对于球体、点质量或点电荷，r 取中心之间的距离，而不是到表面的距离。
- 代入库仑定律与势的公式时保留电荷的正负号；结果为负表示吸引。
- 矢量题必须明确写出方向，因为许多评分标准会为方向单独给分。
- 写对单位：g 用 N kg⁻¹，E 用 N C⁻¹ 或 V m⁻¹，B 用特斯拉 T。
Finally, when a question asks you to compare, always use comparative language: stronger than, opposite to, perpendicular to, does no work whereas. Simply describing each field separately in turn rarely earns full marks.
最后，当题目要求比较时，一定要使用比较性表述：比……更强、与……方向相反、与……垂直、不做功而……。只是分别描述每一种场，通常拿不到满分。
Published by TutorHao | A-Level Physics Revision Series | aleveler.com
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