A-Level AQA Physics: Electric Fields - Key Points | A-Level AQA 物理：电场考点精讲

📚 A-Level AQA Physics: Electric Fields – Key Points | A-Level AQA 物理：电场考点精讲

Electric fields describe the region around a charged object where another charge experiences an electrostatic force. This article covers essential AQA A-level Physics content: Coulomb’s law, electric field strength, potential, equipotentials, and the motion of charged particles, focusing on definitions, equations, and common exam applications.

电场描述了带电物体周围对其他电荷施加静电力的区域。本文涵盖 AQA A-level 物理的核心内容：库仑定律、电场强度、电势、等势面以及带电粒子的运动，重点放在定义、公式及常见考题应用上。

1. Coulomb’s Law | 库仑定律

Coulomb’s law gives 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 magnitude is

F = k Q₁ Q₂ / r²

where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻² and ε₀ is the permittivity of free space. The force acts along the line joining the centres, repulsive for like charges and attractive for opposite charges. In problems involving multiple charges, the net force on a charge is the vector sum of individual Coulomb forces.

库仑定律给出了两点电荷之间的静电力：力的大小与电荷量乘积成正比，与距离的平方成反比。大小为

F = k Q₁ Q₂ / r²

其中 k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻²，ε₀ 是真空介电常数。力的方向沿两电荷连线，同号相斥，异号相吸。在多电荷问题中，某电荷所受的合力为各库仑力的矢量和。

Always use SI units: charge in coulombs (C), distance in metres (m). The constant ε₀ = 8.85 × 10⁻¹² F m⁻¹ is given on the AQA data sheet.

始终使用国际单位：电荷用库仑 (C)，距离用米 (m)。常数 ε₀ = 8.85 × 10⁻¹² F m⁻¹ 在 AQA 公式表中提供。

2. Electric Field Strength | 电场强度

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; its direction is the direction of the force on a positive test charge. The SI unit is N C⁻¹, which is equivalent to V m⁻¹. A uniform field has constant magnitude and direction, while a radial field varies with distance.

电场强度E 定义为放在该点的单位正电荷所受的力：

E = F / q

它是矢量，方向与正检验电荷受力方向相同。国际单位为 N C⁻¹，等同于 V m⁻¹。匀强电场的大小和方向处处相同，而径向电场随距离变化。

To map a field, we imagine a small positive test charge. The force on any charge q in a field is F = qE. This relation holds in both uniform and radial fields.

为描绘电场，可假想一个微小的正检验电荷。任意电荷 q 在电场中所受的力为 F = qE，此关系在匀强场和径向场均成立。

3. Field Due to a Point Charge | 点电荷的电场

For a point charge Q, the electric field strength at a distance r is radial and its magnitude is

E = 1/(4πε₀) × Q / r² = k Q / r²

The field points radially outward from a positive charge and radially inward toward a negative charge. The inverse‑square law means the field strength drops rapidly with distance; doubling the distance reduces E to a quarter. Field lines start on positive charges and end on negative charges.

对于点电荷 Q，在距离 r 处的电场强度沿径向，大小为

E = 1/(4πε₀) × Q / r² = k Q / r²

正电荷的电场径向向外，负电荷的电场径向向内。平方反比律意味着场强随距离增大而迅速减小；距离加倍，E 减小为四分之一。电场线从正电荷出发，终止于负电荷。

When several point charges are present, the resultant electric field at a point is the vector sum of the fields due to each charge. Calculations often require resolving components along perpendicular axes.

当存在多个点电荷时，某点的合电场强度为各点电荷在该点产生的场强的矢量和。计算时常需沿垂直坐标轴分解分量。

4. Uniform Electric Fields and Parallel Plates | 均匀电场与平行板

A uniform electric field is produced between two parallel conducting plates connected to a potential difference V. The field strength is constant and given by

E = V / d

where d is the perpendicular separation of the plates. The direction is from the positive plate to the negative plate. Field lines are equally spaced parallel lines, and a charged particle experiences a constant force F = qE anywhere between the plates (ignoring edge effects).

均匀电场产生于两块连接电势差 V 的平行导电板之间。场强恒定，大小为

E = V / d

其中 d 是板间的垂直距离。方向由正极板指向负极板。电场线是等距的平行线，带电粒子在板间任何位置（忽略边缘效应）都受到恒力 F = qE。

This relationship is also written as E = ΔV / Δx for any uniform field, linking potential difference to field strength. In AQA exam questions, parallel plates are commonly used to accelerate or deflect charged particles.

对于任何均匀场，该关系也可写为 E = ΔV / Δx，将电势差与场强联系起来。在 AQA 考题中，平行板常用来加速或偏转带电粒子。

5. Electric Potential and Potential Energy | 电势与电势能

Electric potential V at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. For a point charge Q,

V = 1/(4πε₀) × Q / r

Potential is a scalar; the potential at a point due to several charges is the algebraic sum of the individual potentials. The potential is zero at an infinite distance. Positive charges produce positive potential, negative charges produce negative potential.

电势 V 是指将单位正电荷从无穷远处移至该点时每单位电荷所做的功。对于点电荷 Q，

V = 1/(4πε₀) × Q / r

电势是标量；多个电荷在某点产生的电势等于各电势的代数和。无穷远处电势为零。正电荷产生正电势，负电荷产生负电势。

Electric potential energy U of a charge q at a point is U = qV. When a charge moves between two points with a potential difference ΔV, the change in potential energy is ΔU = q ΔV. This concept is key to energy conservation in electric fields.

电荷 q 在某点的电势能 U 为 U = qV。当电荷在电势差为 ΔV 的两点间移动时，电势能的变化为 ΔU = q ΔV。这一概念对电场中的能量守恒至关重要。

6. Relationship Between Electric Field and Potential | 电场强度与电势的关系

In a uniform field, the field strength equals the negative potential gradient:

E = – ΔV / Δx

The minus sign shows that the field points in the direction of decreasing potential. For a uniform field between parallel plates, E = V/d, and the potential changes linearly from the positive to the negative plate.

在均匀电场中，场强等于负电势梯度：

E = – ΔV / Δx

负号表示电场指向电势降低的方向。对于平行板间的均匀场，E = V/d，电势由正板到负板线性变化。

In a radial field around a point charge, E = – dV/dr. Differentiating V = kQ/r gives E = kQ/r², consistent with the field strength formula. Where equipotentials are close together, the field is strong; this is used to sketch field strength variations.

在点电荷周围的径向场中，E = – dV/dr。对 V = kQ/r 求导即得 E = kQ/r²，与场强公式一致。等势面密集处场强大，这可用来判断场强的变化。

7. Equipotentials | 等势面

An equipotential surface is a surface on which the electric potential is constant. No work is done by the electric field when a charge moves along an equipotential surface because ΔV = 0. Field lines are always perpendicular to equipotential surfaces.

等势面是电势保持恒定的曲面。电荷沿等势面移动时电场不做功，因为 ΔV = 0。电场线总是垂直于等势面。

Around a point charge, equipotentials are concentric spheres. In a uniform electric field, equipotentials are planes perpendicular to the field lines, equally spaced for equal potential differences. The spacing of equipotentials indicates field strength: the closer the equipotentials, the stronger the field.

在点电荷周围，等势面为同心球面。在均匀电场中，等势面为垂直于电场线的平面，对相等的电势差间距相等。等势面的间距反映了场强大小：等势面越密，场强越大。

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

When a charged particle enters a uniform electric field, its motion can be analysed using kinematic principles. If the initial velocity is perpendicular to the field, the particle follows a parabolic path. The constant electric force F = qE gives a constant acceleration a = qE / m perpendicular to the plates.

当带电粒子进入均匀电场时，可用运动学原理分析其运动。若初速度垂直于电场，则粒子做抛物线运动。恒定的电场力 F = qE 产生垂直于极板的恒定加速度 a = qE / m。

The horizontal component of velocity remains constant, while the vertical component increases linearly with time. The deflection y after travelling a horizontal distance L with speed vₓ is:

y = ½ (qE / m) (L / vₓ)²

This is analogous to projectile motion under gravity, with electric force replacing weight.

水平方向速度分量为常数，垂直方向随时间线性增大。以水平速度 vₓ 水平移动距离 L 后的偏转量 y 为：

y = ½ (qE / m) (L / vₓ)²

这与重力下的抛体运动相似，只是用电场力替代了重力。

If the initial velocity is parallel to the field, the particle accelerates or decelerates along a straight line. Energy methods are often simpler: the change in kinetic energy equals qV, where V is the accelerating potential difference.

若初速度平行于电场，粒子将沿直线加速或减速。此时能量法往往更简便：动能的变化等于 qV，其中 V 为加速电势差。

9. Work Done in Electric Fields | 电场中的功

The work done W by an electric field in moving a charge q through a potential difference ΔV is

W = q ΔV

If the charge moves from rest, this work equals the gain in kinetic energy: ½ m v² = q V. Work done against the electric field is stored as electric potential energy. Since the electric field is conservative, work done is independent of the path taken, depending only on the potential difference between start and end points.

电场移动电荷 q 经过电势差 ΔV 所做的功 W 为

W = q ΔV

若电荷从静止开始运动，该功等于动能的增加量：½ m v² = q V。反抗电场做的功以电势能的形式储存。由于电场是保守场，做的功与路径无关，只取决于起点与终点的电势差。

In a uniform field, the same expression W = qEd cosθ applies, where d is displacement and θ the angle between force and displacement. This links the work–energy principle directly with field parameters.

在匀强电场中，同样有 W = qEd cosθ，其中 d 为位移，θ 为力与位移的夹角。这直接建立了功能原理与电场参数的联系。

10. The Electronvolt | 电子伏特

An electronvolt (eV) is the energy gained by an electron when it is accelerated through a potential difference of 1 volt. By definition:

1 eV = 1.

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A-Level AQA Physics: Electric Fields – Key Points | A-Level AQA 物理：电场 考点精讲