Electric Fields for A2 Physics | A2物理：电场 考点精讲

📚 Electric Fields for A2 Physics | A2物理：电场 考点精讲

Electric fields form one of the cornerstone topics in A2 Physics, linking the concepts of charge, force, energy, and potential. A deep understanding of field lines, field strength, potential, and the motion of charged particles is essential for mastering both theoretical derivations and practical examination questions. This article distils the key points you need to know, with clear definitions, equations, and comparisons to gravitational fields.

电场是A2物理的基石之一，将电荷、力、能量和电势等概念联系在一起。深入理解电场线、场强、电势以及带电粒子的运动，对于掌握理论推导和解题至关重要。本文提炼了你必须掌握的核心考点，给出了清晰的定义、公式以及与引力场的对比。

1. Introduction to Electric Fields | 电场概述

An electric field is a region of space around a charged object where another charged object experiences an electric force. It is a vector field, meaning it has both magnitude and direction at every point. The field exists whether or not a second charge is present to ‘feel’ the force; it is a property of space modified by the source charge.

电场是电荷周围空间中存在的一种特殊物质，在该区域内的其它电荷会受到电场力的作用。电场是一个矢量场，每一点都有大小和方向。无论是否存在检验电荷，电场都存在；它是源电荷对空间性质的一种改变。

2. Coulomb’s Law | 库仑定律

Coulomb’s law gives the magnitude of the force between two point charges: F = k|Q₁Q₂|/r², where k = 1/(4πε₀) ≈ 8.99×10⁹ N·m²/C². The force is attractive if the charges have opposite signs and repulsive if they have the same sign. It follows an inverse‑square relationship with distance, just like Newton’s law of gravitation.

库仑定律描述了两个点电荷之间作用力的大小：F = k|Q₁Q₂|/r²，其中 k = 1/(4πε₀) ≈ 8.99×10⁹ N·m²/C²。同号电荷相互排斥，异号电荷相互吸引。库仑力与距离的平方成反比，这与万有引力定律的形式相似。

3. Electric Field Strength (E) | 电场强度（E）

Electric field strength E at a point is defined as the force per unit positive charge placed at that point: E = F/q. It is a vector quantity measured in N/C or, equivalently, V/m. For a point charge Q, the magnitude of the field a distance r away is E = k|Q|/r². The direction is radially outward from a positive source charge and radially inward toward a negative source charge.

电场强度E定义为某点处单位正电荷所受的力：E = F/q。它是矢量，单位为N/C，也等价于V/m。对于点电荷Q，距离r处的场强大小为E = k|Q|/r²，方向由正电荷沿径向向外，或由负电荷沿径向向内。

4. Electric Field Lines | 电场线

Electric field lines (lines of force) provide a visual representation of the field. Key rules: lines start on positive charges and end on negative charges; the direction of the line at any point gives the direction of the electric field; the density of lines indicates the field strength (closer lines mean stronger field); lines never cross; they are perpendicular to conducting surfaces at equilibrium.

电场线（力线）直观地表示电场。要点：电场线始于正电荷，终于负电荷；线上每点的切线方向表示电场方向；线的疏密反映场强大小（越密越强）；电场线永不相交；静电平衡时，电场线垂直于导体表面。

5. Electric Potential (V) | 电势（V）

Electric potential V at a point is the work done per unit positive charge to move a small test charge from infinity to that point. It is a scalar quantity measured in volts (1 V = 1 J/C). For a point charge Q, V = kQ/r, where potential is taken as zero at infinity. Potential can be positive or negative depending on the sign of Q.

电势V定义为将单位正电荷从无穷远处移至该点时电场力所做的功。电势是标量，单位为伏特（1 V = 1 J/C）。点电荷的电势公式为V = kQ/r，无穷远处电势为零。电势的正负取决于源电荷的符号。

6. Electric Potential Energy | 电势能

Electric potential energy U of a system of two point charges is the work done to assemble the charges from infinite separation: U = kQ₁Q₂/r. This is the energy stored in the configuration. For a charge q moved through a potential difference ΔV, the change in electric potential energy is ΔU = qΔV.

系统的电势能U是将两个点电荷从无穷远处移至相距r时外力所做的功：U = kQ₁Q₂/r。这是储存在位形中的能量。对于在电势差ΔV中移动的电荷q，其电势能的变化量为ΔU = qΔV。

7. Uniform Electric Fields | 匀强电场

A uniform electric field has the same magnitude and direction at all points. It is produced by two parallel conducting plates with a potential difference V between them, separated by a distance d. The field strength is constant: E = V/d. Field lines are parallel, equally spaced, and directed from the positive plate to the negative plate.

匀强电场中各点的场强大小和方向均相同。它由两块保持电势差V、相距d的平行导体板产生。场强大小为E = V/d，恒定不变。电场线为一系列平行且等间距的直线，方向由正极板指向负极板。

8. Point Charge Electric Fields | 点电荷的电场

For a single point charge, both E and V follow radial dependencies: E ∝ 1/r², V ∝ 1/r. This means the field strength drops off more rapidly with distance than the potential does. In diagrams, equipotential surfaces around a point charge are concentric spheres, always perpendicular to field lines.

对于单个点电荷，E和V随距离的变化规律不同：E ∝ 1/r²，而 V ∝ 1/r。这意味着场强随距离衰减得比电势更快。在示意图中，点电荷周围的等势面是同心球面，且始终与电场线垂直。

9. Relationship between E and V (Potential Gradient) | 电场强度与电势的关系（电势梯度）

In general, the electric field is the negative gradient of the potential: E = -dV/dr (in one dimension). This means E points in the direction of the steepest decrease in potential. In a uniform field, this reduces to E = V/d. The minus sign indicates that a positive charge accelerates from high to low potential.

一般情况下，电场强度等于电势梯度的负值：E = -dV/dr（一维情形）。这意味着E指向电势下降最快的方向。在匀强电场中，该关系简化为E = V/d。负号表示正电荷会从高电势加速移向低电势。

10. Motion of Charged Particles in Electric Fields | 带电粒子在电场中的运动

A charged particle of charge q in an electric field E experiences a force F = qE, leading to an acceleration a = qE/m. In a uniform field, motion can be analysed using kinematic equations. For an electron entering a uniform field perpendicularly, it follows a parabolic path, analogous to projectile motion under gravity, because the lateral deflection is constant acceleration while the horizontal velocity remains constant.

电荷q在电场E中受到的力为F = qE，因而加速度为a = qE/m。在匀强电场中，可以用运动学方程分析其运动。当电子垂直射入匀强电场时，它将作类平抛的抛物线运动，因为侧向加速度恒定，而水平速度保持不变。

11. Comparison of Gravitational and Electric Fields | 引力场与电场的比较

Both fields follow inverse‑square force laws (Newton’s law and Coulomb’s law), have potentials that vary as 1/r, and have a field strength defined as force per unit property (mass or charge). Key differences: mass is always positive whereas charge can be positive or negative; gravitational forces are always attractive, electric forces can be attractive or repulsive; electric fields can be shielded, while gravitational fields cannot.

引力场和电场都遵循平方反比定律（万有引力定律和库仑定律），电势均按1/r变化，场强都定义为每单位属性（质量或电荷）所受的力。主要区别在于：质量恒正，电荷可正可负；引力始终是吸引力，电场力可以是吸引或排斥；电场可以被屏蔽，引力场不能。

12. Summary and Exam Tips | 总结与应试技巧

Remember the key formulae: E = F/q, E = V/d (uniform), E = kQ/r² (point charge), V = kQ/r, ΔU = qΔV. Always pay attention to the vector nature of E and the scalar nature of V. Use the principle of superposition for multiple charges. In exam problems, clearly state the sign of charges and show the direction of forces or fields with arrows. Practise deriving the motion of charged particles in parallel fields and recognising the analogy to projectile motion.

牢记核心公式：E = F/q，匀强电场E = V/d，点电荷E = kQ/r²，V = kQ/r，ΔU = qΔV。务必注意E的矢量性与V的标量性，并运用叠加原理处理多个电荷。解题时明确写出电荷正负，用箭头标示力或场的方向。多练习带电粒子在匀强电场中的运动分析，熟悉它与抛体运动的类比。

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Published by TutorHao | Physics Revision Series | aleveler.com

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