A-Level OCR Physics: Electric Fields Revision Notes | A-Level OCR 物理：电场考点精讲

📚 A-Level OCR Physics: Electric Fields Revision Notes | A-Level OCR 物理：电场考点精讲

Electric fields lie at the heart of many A-Level Physics topics, from atomic structure to circuits. In this OCR revision guide, we break down every essential concept, equation and experiment you need to master for the exam. Whether it’s Coulomb’s law, uniform fields between parallel plates or Millikan’s oil drop, you’ll find clear explanations and real exam focus.

电场是许多A-Level物理主题的核心，从原子结构到电路分析都离不开它。在这篇OCR考点精讲中，我们会逐一拆解你需要掌握的每一个关键概念、公式和实验。无论是库仑定律、平行板间的匀强电场还是密立根油滴实验，你都可以找到清晰的讲解和直击考点的分析。

1. Electric Field Basics | 电场基础知识

An electric field is a region of space where a stationary charged particle experiences an electric force. The field is produced by source charges and is a vector quantity, having both magnitude and direction at every point.

电场是一个空间区域，静止电荷会在其中受到电场力。该场由源电荷产生，是矢量量，在每一点都有大小和方向。

We define the direction of an electric field as the direction of the force that a small positive test charge (+q) would experience if placed at that point. This convention makes field lines point away from positive charges and toward negative charges.

我们定义电场的方向为放置在该点的小正检验电荷（+q）所受力的方向。这一规定使电场线从正电荷指向负电荷。

2. Coulomb’s Law | 库仑定律

Coulomb’s law gives the magnitude of the force between two point charges Q₁ and Q₂ separated by distance r in a vacuum: directly proportional to the product of the charges and inversely proportional to the square of the distance.

库仑定律给出了真空中相距r的两个点电荷Q₁和Q₂之间力的大小：力与电荷乘积成正比，与距离平方成反比。

F = (1 / (4π ε₀)) × (Q₁Q₂ / r²)

F = (1 / (4π ε₀)) · (Q₁Q₂ / r²)

The constant ε₀ is the permittivity of free space, ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹. The forces are attractive if the charges have opposite signs and repulsive if they have the same sign.

常数ε₀是自由空间介电常数，ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹。电荷异号时力为吸引，同号时为排斥。

3. Electric Field Strength | 电场强度

Electric field strength (E) at a point is the force per unit positive charge experienced by a small test charge placed at that point:

电场强度（E）定义为置于该点的小检验电荷每单位正电荷所受的力：

E = F / q

Its SI unit is N C⁻¹ (equivalent to V m⁻¹). E is a vector; its direction is the same as the force on a positive test charge.

其国际单位是 N C⁻¹（相当于 V m⁻¹）。E是矢量，方向与正检验电荷受力方向相同。

For a point charge Q, the field strength at a distance r is:

对于点电荷Q，距离r处的电场强度为：

E = (1 / (4π ε₀)) × (Q / r²)

In a uniform electric field between two parallel plates, the field strength is constant and given by the potential difference V and plate separation d:

在两平行板之间的匀强电场中，场强恒定，与电势差V和板间距d的关系为：

E = V / d

4. Electric Field Lines | 电场线

Field lines are a visual tool to represent electric fields. They begin on positive charges and end on negative charges, never forming closed loops. The tangent to a line at any point shows the direction of the field, and the density of lines indicates the field strength.

电场线是表示电场的可视化工具。它们始于正电荷，终止于负电荷，不形成闭合曲线。线上任一点的切线方向表示该点的场强方向，线的疏密程度表示场强的大小。

Key rules: field lines do not cross; they are perpendicular to the surface of a conductor at equilibrium; and in a uniform field they appear as equally spaced parallel lines.

关键规则：电场线不相交；平衡状态导体外表面处电场线垂直于表面；在匀强电场中，它们表现为等间距的平行直线。

5. Uniform Electric Fields and Parallel Plates | 匀强电场与平行板

A uniform electric field has the same magnitude and direction everywhere in a region. This is closely approximated by two parallel conducting plates with a constant potential difference V across them, separated by distance d.

匀强电场在区域内各处的大小和方向均相同。两平行导体板间保持恒定电势差V、间距为d时，可很好地近似为匀强电场。

The field strength is E = V/d, and the field direction is from the positive plate (higher potential) to the negative plate (lower potential). Charged particles in such a field experience a constant electric force F = qE.

场强大小为 E = V/d，方向从正极板（高电势）指向负极板（低电势）。处于该场中的带电粒子受到恒定的电场力 F = qE。

This arrangement is used in particle accelerators, ink-jet printers and cathode-ray tubes to deflect charged beams.

这种装置用于粒子加速器、喷墨打印机和阴极射线管，以偏转带电束流。

6. 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, without any change in kinetic energy. It is a scalar quantity measured in volts (V), where 1 V = 1 J C⁻¹.

电势（V）是指将小正检验电荷从无穷远移至该点所做的功（每单位正电荷），且过程中动能不变。它是标量，单位为伏特（V），1 V = 1 J C⁻¹。

For a point charge Q, the potential at distance r is:

对于点电荷Q，距离r处的电势为：

V = (1 / (4π ε₀)) × (Q / r)

The electric potential energy (U) of a charge q at a point where the potential is V is U = qV. When charges move through a potential difference ΔV, the change in potential energy is ΔU = q ΔV.

电荷q在电势为V处的电势能为 U = qV。当电荷通过电势差ΔV时，电势能的变化为 ΔU = q ΔV。

7. Relationship Between Field and Potential | 场与电势的关系

In a non-uniform field, the electric field strength is the negative of the potential gradient:

在非匀强电场中，电场强度是电势梯度的负值：

E = − dV / dr

This means the field points in the direction of steepest decrease in potential. For a uniform field, this reduces to E = −ΔV/Δd, so the magnitude is simply ΔV/d with direction from higher to lower potential.

这意味着场的方向指向电势下降最快的方向。对于匀强电场，这简化为 E = −ΔV/Δd，因此大小就是 ΔV/d，方向由高电势指向低电势。

Understanding this link helps you move between E–r and V–r graphs for point charges and uniform fields.

理解这一联系有助于你在点电荷和匀强电场的 E–r 图和 V–r 图之间转换。

8. Equipotential Surfaces | 等势面

An equipotential surface is a surface on which the electric potential is the same everywhere. No work is required to move a charge along an equipotential surface because the potential difference is zero.

等势面是上面所有点电势都相同的面。由于电势差为零，电荷沿等势面移动时不需要做功。

Equipotential surfaces are always perpendicular to electric field lines. Around an isolated point charge they are concentric spheres; between uniform parallel plates they are planes parallel to the plates.

等势面始终垂直于电场线。孤立点电荷周围的等势面是同心球面；在匀强平行板之间，它们是平行于极板的平面。

9. 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 at right angles, its motion mimics that of a projectile in a gravitational field. The constant electric force produces a constant acceleration in the field direction, while velocity parallel to the plates remains unchanged.

当带电粒子垂直进入匀强电场时，其运动类似于引力场中的抛体运动。恒定的电场力在电场方向上产生恒定加速度，而平行于极板的速度分量保持不变。

For an electron (charge −e) injected with speed v₀ into a field of strength E over a horizontal length L, the vertical deflection y is:

对于以速度v₀射入电场E中的电子（电荷−e），水平长度为L时，垂直偏转量y为：

y = ½ (eE / m) (L / v₀)²

The angular deflection θ satisfies tanθ = (eEL) / (m v₀²). These relationships are vital for understanding devices like oscilloscopes.

偏转角θ满足 tanθ = (eEL) / (m v₀²)。这些关系对于理解示波器等设备至关重要。

10. Millikan’s Oil Drop Experiment | 密立根油滴实验

Millikan’s experiment determined the fundamental unit of charge, e, by balancing tiny charged oil drops between parallel plates. When the drop is stationary, the electric force qE equals the weight mg minus the upthrust (often negligible).

密立根实验通过平衡平行板间微小带电油滴，测定了基本电荷e。当油滴静止时，电场力qE等于重力mg减浮力（通常可忽略）。

Using E = V/d, the charge carried by the drop is:

利用 E = V/d，油滴所带电荷为：

q = mgd / V

Millikan found that all charges were integer multiples of e ≈ 1.60 × 10⁻¹⁹ C, proving charge quantisation. Students must be able to explain the experimental procedure and calculate q and e from given data.

密立根发现所有电荷都是 e ≈ 1.60 × 10⁻¹⁹ C 的整数倍，证明了电荷的量子化。考生必须能够解释实验步骤并根据数据计算q和e。

11. Comparison of Electric and Gravitational Fields | 电场与引力场的类比

Electric and gravitational fields share many similarities, but also have crucial differences. The table below highlights the key comparisons relevant to OCR exams.

电场与引力场有许多相似之处，但也有关键区别。下表突出了与OCR考试相关的重要对比。

Property	Gravitational Field	Electric Field
Source	Mass	Charge
Force law	F = G m₁m₂ / r² (always attractive)	F = (1/4π ε₀) Q₁Q₂ / r² (attractive or repulsive)
Field strength	g = F/m (N kg⁻¹)	E = F/q (N C⁻¹)
Potential	V_g = −G M / r (scalar)	V = (1/4π ε₀) Q / r (scalar, can be + or −)
Uniform field	g ≈ constant near Earth’s surface	E = V/d between parallel plates

Both obey inverse-square laws and have equipotential surfaces perpendicular to field lines. However, only electric fields can be shielded and can exert forces on stationary particles without requiring a mass.

两者都遵循平方反比定律，且等势面与场线垂直。然而，只有电场可以被屏蔽，且能在不要求有质量的情况下对静止粒子施加力。

12. Key Equations and Summary | 关键方程与总结

Mastering electric fields requires fluency with the following equations. Practice applying them to different scenarios, such as oil drop problems, deflection tubes and radial field graphs.

掌握电场需要熟练运用以下方程。练习将它们应用于不同场景，如油滴问题、偏转管和径向场图像。

• Coulomb’s law: F = Q₁Q₂ / (4π ε₀ r²) | 库仑定律：F = Q₁Q₂ / (4π ε₀ r²)
• Field strength definition: E = F/q | 场强定义：E = F/q
• Radial field: E = Q / (4π ε₀ r²) | 径向场：E = Q / (4π ε₀ r²)
• Uniform field: E = V/d | 匀强电场：E = V/d
• Potential (point charge): V = Q / (4π ε₀ r) | 电势（点电荷）：V = Q / (4π ε₀ r)
• Potential energy: ΔU = q ΔV | 电势能：ΔU = q ΔV
• Field–potential gradient: E = − dV/dr | 场与电势梯度：E = − dV/dr
• Deflection (electron): y = ½ (eE/m) (L/v₀)² | 偏转（电子）：y = ½ (eE/m) (L/v₀)²
• Millikan’s condition: q = mgd / V | 密立根条件：q = mgd / V

Always remember to include directions for vectors, use SI units and treat potential as a scalar superposition. With this structured revision, you are now equipped to tackle any OCR electric fields question with confidence.

务必记住矢量要标明方向，使用国际单位制，并注意电势是标量叠加。通过这份结构化复习，你现在已有信心应对任何OCR电场考题。

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