📚 Electric Fields: Key Concepts for IB & AQA Physics | 电场：IB 和 AQA 物理考点精讲
Electric fields underpin much of electromagnetism and are a central topic in both IB and AQA Physics. This revision guide breaks down the essential concepts, equations, and common exam pitfalls to help you master the topic.
电场是电磁学的基础，也是 IB 和 AQA 物理的核心考点。本复习指南将剖析关键概念、重要公式和常见考试陷阱，帮助大家彻底掌握该主题。
1. What is an Electric Field? | 电场是什么？
An electric field is a region in space around a charged object where any other charged object experiences an electric force.
电场是带电物体周围空间中，其他带电物体会受到电场力的区域。
It is a vector field, meaning it has both magnitude and direction at every point. The direction of the field is defined as the direction of the force on a small positive test charge placed at that point.
它是一种矢量场，即在每个点上都有大小和方向。场的方向被定义为置于该点的小正检验电荷所受力的方向。
Electric field lines (lines of force) are used to visualise the field. They begin on positive charges and end on negative charges, never cross, and their density represents field strength.
电场线（力线）用来直观表示电场。它们从正电荷出发，终止于负电荷，永不相交，线的密度表示场强。
2. Electric Field Strength (E) | 电场强度
Electric field strength is defined as the force per unit positive charge: E = F / q. It is a vector quantity.
电场强度定义为单位正电荷所受的力：E = F / q。它是矢量。
The SI unit is newton per coulomb (N C⁻³) which is equivalent to volt per metre (V m⁻³).
国际单位是牛顿每库仑 (N C⁻³)，也等于伏特每米 (V m⁻³)。
₀. The direction of E is the same as the force direction on a positive charge and opposite for a negative charge.
如果检验电荷 q₀ 受到力 F₀，则该点场强 E = F₀/q₀。E 的方向与正电荷受力方向相同，与负电荷受力方向相反。
E = F / q
3. Electric Field of a Point Charge | 点电荷的电场
The magnitude of the electric field at a distance r from a point charge Q is given by Coulomb's law: E = k |Q| / r², where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻³.
距离点电荷 Q 为 r 处的电场强度大小由库仑定律给出：E = k |Q| / r²，其中 k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻³。
The field is radial: for a positive source charge, E points radially outward; for a negative source charge, E points radially inward.
电场是径向的：对于正源电荷，E 沿径向向外；对于负源电荷，E 沿径向向内。
The electric field outside a uniformly charged sphere is identical to that of a point charge located at its centre.
均匀带电球体外部的电场与一个位于球心的点电荷的电场完全相同。
E = k Q / r² k = 1/(4πε₀)
4. Uniform Electric Fields | 匀强电场
A uniform electric field has the same magnitude and direction at all points. It is approximately produced between two parallel conducting plates connected to a potential difference V.
匀强电场中各点的场强大小和方向都相同。它近似由连接电势差 V 的两块平行导体板产生。
The electric field strength in a uniform field is related to the plate separation d by E = V / d is is derived from the work done moving a charge: W = F d = q E d and W = q V, so V = E d.
匀强电场中的场强与板间距 d 的关系为 E = V / d。这可以从移动电荷做功推导：W = F d = q E d 且 W = q V，因此 V = E d。
Field lines are equally spaced parallel lines, pointing from the positive plate towards the negative plate.
电场线为等距的平行线，从正极板指向负极板。
E = V / d
5. Electric Potential (V) | 电势
Electric potential at a point is the electric potential energy per unit charge carried by a small positive test charge placed at that point: V = Eₚ / q. It is a scalar quantity.
电势是置于该点的小正检验电荷每单位电荷所具有的电势能：V = Eₚ / q。它是标量。
The potential at a distance r from a point charge Q (with zero at infinity) is V = k Q / r. The potential due to several charges is the algebraic sum of individual potentials.
距点电荷 Q 为 r 处的电势（无穷远处为零）为 V = k Q / r。多个电荷产生的电势是各电势的代数和。
In a uniform electric field, the potential decreases uniformly in the direction of the field.
在匀强电场中，电势沿电场方向均匀降低。
V = k Q / r
6. Electric Potential Energy | 电势能
The electric potential energy of a charge q at a point where the electric potential is V is Eₚ = q V.
电荷 q 在电势为 V 的点具有的电势能为 Eₚ = q V。
- Vₙ) if we define the work done against the field appropriately. Essentially ΔEₚ = q ΔV.
电场将电荷从 A 点移动到 B 点所做的功与电势能变化的关系为 ΔEₚ = q (Vₙ - Vₐ) 等等，核心是 ΔEₚ = q ΔV。
A convenient unit of energy in atomic systems is the electronvolt (eV): 1 eV is the energy gained by an electron when it moves through a potential difference of 1 V.
在原子系统中方便的能单位是电子伏特 (eV)：1 eV 是一个电子经过 1 V 电势差加速后获得的能量。
7. Relationship between E and V | 电场强度与电势的关系
In general, the electric field is the negative gradient of the electric potential: E = -dV / dr in the radial direction for a point charge, or E = -ΔV / Δx for a uniform field along the direction of the field.
一般来说，电场是电势的负梯度：点电荷沿径向有 E = -dV / dr，匀强场中沿场方向有 E = -ΔV / Δx。
The field points in the direction of the steepest decrease of potential. Equipotential surfaces are perpendicular to the field lines because no work is done when moving along an equipotential.
电场指向电势下降最快的方向。等势面与电场线垂直，因为沿等势面移动电荷不做功。
E = -ΔV / Δx
8. Motion of Charged Particles in an Electric Field | 带电粒子在电场中的运动
iform electric field gains kinetic energy: W = q V = ½ m v², assuming it starts from rest.
带电粒子在匀强电场中被加速时获得的动能：W = q V = ½ m v²，假设从静止开始。
tant while the vertical component accelerates uniformly due to the electric force F = q E.
如果带电粒子垂直于电场线进入匀强电场，它将做抛物线运动（类似抛体运动）。水平速度分量不变，竖直分量由于电场力 F = q E 而均匀加速。
The vertical deflection y after travelling a horizontal distance L is given by: y = (q E L²) / (2 m v²), where v is the initial speed.
水平移动距离 L 后的竖直偏转量 y 为：y = (q E L²) / (2 m v²)，其中 v 是初速度。
This principle is used in cathode ray tubes and particle accelerators for controlled deflection.
这一原理被用于阴极射线管和粒子加速器中的可控偏转。
9. Equipotential Surfaces | 等势面
done to move a charge along an equipotential surface because ΔV = 0 and thus W = q ΔV = 0.
等势面是电势恒定的面。沿等势面移动电荷不做功，因为 ΔV = 0，所以 W = q ΔV = 0。
Field lines always intersect equipotential surfaces at right angles. The closer the equipotentials, the stronger the electric field (the larger the potential gradient).
电场线总与等势面垂直相交。等势面越密集，电场越强（电势梯度越大）。
For a point charge, equipotentials are concentric spheres. In a uniform field, equipotentials are equally spaced parallel planes.
对于点电荷，等势面是同心的球面。在匀强电场中，等势面是等距的平行平面。
10. Comparison between Electric and Gravitational Fields | 电场与引力场的比较
Both electric and gravitational fields follow inverse-square laws for their field strengths. However, while gravitational forces are always attractive, electric forces can be attractive or repulsive. This table summarises the key comparisons.
电场和引力场的场强都遵循平方反比律。然而，引力总是吸引的，而电场力可以是吸引或排斥的。下表总结了关键对比。
| Property | Electric Field | Gravitational Field |
|---|---|---|
| Source | Charge Q | Mass M |
| Force Law | F = k Q q / r² | F = G M m / r² |
| Field Strength | E = k Q / r² (N C⁻³) | g = G M / r² (N kg⁻³) |
| Potential | V = k Q / r (scalar) | V₉ = -G M / r |
| Nature | Attractive or repulsive | Always attractive |
| Shielding | Can be shielded | Cannot be shielded |
Grasping these parallels and distinctions is a common exam requirement. Both fields store energy and can do work, but the sign of the potential energy depends on the sign of charges.
掌握这些异同是常见的考试要求。两种场都能储存能量并做功，但电势能的符号取决于电荷的正负。
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