Electric Fields in A-Level WJEC Physics | A-Level WJEC 物理：电场考点精讲

📚 Electric Fields in A-Level WJEC Physics | A-Level WJEC 物理：电场考点精讲

Understanding electric fields is fundamental in A-Level WJEC Physics. This guide reviews the key concepts you need to master, from Coulomb’s law to uniform fields, potential, and the motion of charged particles. Each section gives you a clear explanation, typical exam applications, and the essential equations without any clutter.

电场是 A-Level WJEC 物理的基础内容。本文梳理了从库仑定律到匀强电场、电势以及带电粒子运动等核心考点，每节都提供清晰的解释、典型考试应用和关键公式，帮助你高效备考。

1. Electric Charge and Coulomb’s Law | 电荷与库仑定律

All electric phenomena arise from electric charge. There are two types: positive and negative. Like charges repel, and unlike charges attract. The force between two point charges Q₁ and Q₂ separated by distance r is given by Coulomb’s law: F = k Q₁Q₂ / r², where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻², and ε₀ is the permittivity of free space.

所有电现象源于电荷。电荷分正负两种，同性相斥、异性相吸。两个点电荷 Q₁ 与 Q₂ 相距 r 时的作用力由库仑定律描述：F = k Q₁Q₂ / r²，k = 1/(4πε₀) ≈ 8.99×10⁹ N m² C⁻²，ε₀ 是真空介电常数。

The force is along the line joining the two charges. If the charges are in a vacuum, ε₀ = 8.85×10⁻¹² F m⁻¹. Often you will use the form F = (1/(4πε₀)) × (Q₁Q₂ / r²).

力的方向沿两电荷连线。真空中 ε₀ = 8.85×10⁻¹² F m⁻¹。通常公式写作 F = (1/(4πε₀)) × (Q₁Q₂ / r²)。

2. Electric Field Definition | 电场强度的定义

An electric field is a region in which an electric charge experiences a force. The electric field strength E at a point is defined as the force per unit positive charge: E = F / q. It is a vector quantity, measured in N C⁻¹ or equivalently V m⁻¹.

电场是电荷受力的区域。电场强度 E 定义为某点单位正电荷所受的力：E = F / q。它是一个矢量，单位为 N C⁻¹，也可用 V m⁻¹。

This definition works for any field, whether uniform or radial. The direction of E is the direction of the force on a positive test charge.

这个定义适用于任何电场，匀强或辐射状。E 的方向就是正检验电荷受力的方向。

3. Electric Field Lines | 电场线

Field lines represent the electric field visually. They start on positive charges and end on negative charges. The density of lines indicates field strength, and the tangent at any point gives the direction of E. Field lines never cross.

电场线形象表示电场。它们从正电荷出发，终止于负电荷。线密度表示场强大小，某点的切线方向就是 E 的方向。电场线永不相交。

In a uniform field, lines are parallel and equally spaced. Around an isolated point charge, lines are radial: outward for positive, inward for negative.

匀强电场中，线平行且等距。孤立点电荷周围呈径向：正电荷向外，负电荷向内。

4. Electric Field Due to a Point Charge | 点电荷的电场强度

For a single point charge Q, the electric field strength at a distance r is E = (1/(4πε₀)) × (Q / r²). This is derived from Coulomb’s law by placing a test charge q and using E = F/q.

对单个点电荷 Q，距离 r 处的电场强度为 E = (1/(4πε₀)) × (Q / r²)。这由库仑定律和 E = F/q 推导得出。

The field points away from a positive Q and towards a negative Q. E follows an inverse-square law: doubling the distance reduces E to one quarter.

Q 为正时，E 方向背离电荷；负则指向电荷。E 遵循反平方律：距离加倍，场强减为四分之一。

5. Uniform Electric Fields | 匀强电场

A uniform electric field exists between two parallel conducting plates connected to a potential difference V, separated by distance d. The field is constant in magnitude and direction: E = V / d.

两块平行导体板接上电势差 V，相距 d，之间就产生匀强电场。场的大小和方向处处相同：E = V / d。

This equation gives E in V m⁻¹, showing the two units are identical. A charged particle in such a field experiences a constant force F = qE = qV/d, leading to parabolic trajectories similar to projectile motion under gravity.

该式给出 E 的单位 V m⁻¹，与 N C⁻¹ 等价。带电粒子在匀强电场中受恒力 F = qE = qV/d，运动轨迹呈抛物线，类似重力场中的抛体运动。

6. Potential Difference and Work Done | 电势差与做功

The potential difference ΔV between two points is the work done per unit charge to move a positive test charge between them: ΔV = W / q. In a uniform field, work is also W = F d = qE d, giving ΔV = E d when moving along the field direction.

两点间电势差 ΔV 是将单位正电荷从一点移到另一点所做的功：ΔV = W / q。在匀强电场中，沿电场方向移动时做功 W = F d = qE d，因此 ΔV = E d。

If the movement is at an angle θ to the field, the component d cosθ is used: ΔV = E d cosθ. This is closely linked to the concept of electric potential.

若移动方向与电场夹角为 θ，则有效距离为 d cosθ：ΔV = E d cosθ。这与电势概念紧密相连。

7. Electric Potential | 电势

Electric potential V at a point is the work done per unit charge to bring a positive test charge from infinity to that point. For a point charge Q, the potential is V = (1/(4πε₀)) × (Q / r). Potential is a scalar, measured in volts (J C⁻¹).

某点的电势 V 是将单位正电荷从无穷远移到该点所做的功。点电荷 Q 产生的电势为 V = (1/(4πε₀)) × (Q / r)。电势是标量，单位是伏特 (J C⁻¹)。

The potential at infinity is taken as zero. Around a positive charge, potentials are positive; around a negative charge, negative. The total potential at a point due to several charges is the algebraic sum.

无穷远处电势取为零。正电荷周围电势为正，负电荷为负。多个电荷产生的电势为代数和。

8. Electric Potential Energy | 电势能

The electric potential energy U of a charge q placed at a point with potential V is U = q V. For two point charges Q and q separated by distance r, the potential energy of the system is U = (1/(4πε₀)) × (Q q / r).

电荷 q 在电势 V 处具有的电势能是 U = q V。两个点电荷 Q 与 q 相距 r 时，系统电势能为 U = (1/(4πε₀)) × (Q q / r)。

If the charges have the same sign, U is positive (repulsion); opposite signs give negative U (attraction). Change in potential energy equals work done by or against the electric field.

同号电荷，U 为正（排斥）；异号为负（吸引）。电势能的变化等于电场力做的功或克服电场力做的功。

9. Equipotential Surfaces | 等势面

Equipotential surfaces are surfaces where the electric potential is constant. No work is done moving a charge along an equipotential. Field lines are always perpendicular to equipotential surfaces.

等势面是电势处处相等的面。电荷沿等势面移动时不做功。电场线处处垂直于等势面。

For a point charge, equipotentials are concentric spheres. In a uniform field, they are parallel planes perpendicular to the field lines. The spacing of equipotentials shows the field strength: closer spacing means stronger field.

点电荷的等势面是同心球面。匀强电场中，等势面是垂直于电场线的平行平面。等势面的疏密反映场强：间距越小，场强越大。

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

When a charged particle enters an electric field, it accelerates according to F = qE. In a uniform field parallel to its initial velocity, the particle undergoes linear acceleration, and energy conservation gives ½ m v² = q V (if starting from rest or with initial kinetic energy changing by qΔV).

带电粒子进入电场后，按 F = qE 加速。当初速度与匀强电场平行时，粒子做直线加速，能量守恒得 ½ m v² = q V（从静止出发，或动能变化等于 qΔV）。

If the particle enters perpendicular to a uniform field, it follows a parabolic path, like a horizontal projectile. Horizontal velocity remains constant, while vertical acceleration is a = qE/m. This principle is used in cathode ray tubes and particle deflection experiments.

粒子垂直进入匀强电场时，轨迹为抛物线，类似平抛运动。水平速度不变，竖直加速度为 a = qE/m。此原理应用于阴极射线管和粒子偏转实验。

11. Comparison with Gravitational Fields | 电场与引力场的比较

Electric and gravitational fields share many mathematical similarities, but there are key differences. Both follow inverse-square laws for point sources. Electric field strength E and gravitational field strength g are both defined as force per unit property (charge vs mass).

电场和引力场在数学上有很多相似之处，但存在关键差异。点源都遵循反平方律。电场强度 E 和引力场强度 g 都定义为单位属性（电荷 vs 质量）所受的力。

Potential at a point is V = (1/(4πε₀)) Q/r vs gravitational potential V_g = – GM/r. Unlike gravity, which is always attractive, electric forces can be attractive or repulsive. Also, G is universal, whereas 1/(4πε₀) depends on the medium.

点源电势 V = (1/(4πε₀)) Q/r，而引力势 V_g = -GM/r。引力总是吸引，电力可以是引力也可以是斥力。此外，G 是普适常数，1/(4πε₀) 则依赖于介质。

12. Key Equations Summary and Exam Tips | 公式总结与考试技巧

Memorise these essential equations: E = F/q, E = (1/(4πε₀)) Q/r², E = V/d, V = (1/(4πε₀)) Q/r, W = qΔV, F = (1/(4πε₀)) Q₁Q₂/r². In exams, always state the law or definition before substituting values. Watch unit conversions: distance in metres, charge in coulombs.

牢记这些关键公式：E = F/q、E = (1/(4πε₀)) Q/r²、E = V/d、V = (1/(4πε₀)) Q/r、W = qΔV、F = (1/(4πε₀)) Q₁Q₂/r²。考试中先写出定律或定义再代入数值。注意单位换算：距离用米，电荷用库仑。

For multi-step problems, sketch field lines or equipotentials to visualise the situation. When combining forces or fields from multiple charges, treat vectors correctly. Practise explaining the similarities and differences between electric and gravitational fields, as this is a common WJEC comparison question.

多步问题可画电场线或等势面帮助分析。处理多个电荷的力或场时，注意矢量叠加。练习比较电场与引力场的异同，这是 WJEC 常见的对比题型。

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Electric Fields in A-Level WJEC Physics | A-Level WJEC 物理：电场 考点精讲