Unit 4: Electric Fields and Capacitors | 第4单元：电场与电容器

📚 Unit 4: Electric Fields and Capacitors | 第4单元：电场与电容器

This unit develops core ideas in electrostatics and capacitor circuits. You will learn how electric fields arise from charges, how potential difference relates to work, how capacitors store charge and energy, and how RC circuits behave during charging and discharging.

本单元拓展静电学与电容器电路的核心概念。你将学习电场如何由电荷产生、电势差与功的关系、电容器如何储存电荷和能量，以及 RC 电路在充放电过程中的行为。

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1. Electric Fields and Field Strength | 电场与电场强度

An electric field is a region where a charged object experiences an electrostatic force. Electric field strength E is defined as the force F acting per unit positive charge q placed at that point.

电场是带电物体受到静电力的区域。电场强度 E 定义为放置在电场中某点的单位正电荷所受的力 F。

E = F ÷ q

The SI unit of electric field strength is newton per coulomb (N C⁻¹). It is also equivalent to volt per metre (V m⁻¹), which is useful when linking electric fields to potential difference.

电场强度的国际单位是牛每库仑（N C⁻¹）。它也等价于伏特每米（V m⁻¹），在联系电场与电势差时非常有用。

Electric field lines show the direction of the force on a small positive test charge. They point away from positive charges and toward negative charges. The closer the field lines are, the stronger the electric field.

电场线表示小的正检验电荷所受力的方向。它们从正电荷发出并指向负电荷，电场线越密集表示电场越强。

Electric field is a vector quantity. When two or more fields overlap, the resultant field at a point is found by vector addition.

电场是矢量。当两个或多个电场叠加时，某点的合电场通过矢量加法求得。

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2. Coulomb’s Law | 库仑定律

Coulomb’s law gives the force between two point charges Q and q separated by a distance r. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance.

库仑定律给出两个点电荷 Q 和 q 在距离 r 时的作用力。力与电荷乘积成正比，与距离的平方成反比。

F = kQq ÷ r²

The constant k is equal to 1/(4πε₀), where ε₀ is the permittivity of free space. Numerically, k ≈ 8.99 × 10⁹ N m² C⁻².

常数 k 等于 1/(4πε₀)，其中 ε₀ 为真空介电常数。数值上 k ≈ 8.99 × 10⁹ N m² C⁻²。

For two like charges the force is repulsive, and for two opposite charges the force is attractive. Coulomb’s law is an inverse-square law, so doubling the separation reduces the force to one quarter of its original value.

同种电荷之间的力为排斥力，异种电荷之间的力为吸引力。库仑定律是平方反比定律，因此距离翻倍会使力减少到原来的四分之一。

The law applies strictly to point charges or to spherically symmetric charge distributions. In exam problems, charged spheres can often be treated as point charges located at their centres.

该定律严格适用于点电荷或球对称电荷分布。在考试题中，带电球体通常可以视为电荷集中于球心的点电荷。

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3. Electric Potential and Potential Difference | 电势与电势差

Electric potential V at a point in an electric field is the work done per unit positive charge in bringing a small positive test charge from infinity to that point.

电场中某点的电势 V 是将小的正检验电荷从无穷远移到该点时每单位正电荷所做的功。

V = W ÷ q

Electric potential is a scalar quantity and is measured in volts. One volt is one joule per coulomb. Potential can be positive or negative depending on the source charge.

电势是标量，单位为伏特。1 伏特等于 1 焦耳每库仑。根据源电荷的正负，电势可以是正值或负值。

The potential difference between two points A and B is V_A − V_B, and it represents the work done per unit charge moving from B to A.

两点 A 与 B 之间的电势差为 V_A − V_B，表示将单位电荷从 B 移到 A 所做的功。

Equipotential surfaces are surfaces on which the potential is constant. No work is done when a charge moves along an equipotential surface. Equipotentials are always perpendicular to electric field lines.

等势面是电势恒定的曲面。电荷沿等势面移动时不做功。等势面总是与电场线垂直。

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4. Uniform Electric Fields | 均匀电场

A uniform electric field is produced between two oppositely charged parallel plates. The field strength is the same at all points between the plates, and the field lines are parallel and equally spaced.

两个带相反电荷的平行板之间产生均匀电场。两极板之间各点场强相同，电场线平行且等间距。

E = V ÷ d

Here V is the potential difference between the plates and d is their separation. This equation is often used with the definition E = F/q to calculate the force on a charged particle in a uniform field.

式中 V 为两极板间的电势差，d 为板间距。该公式常与 E = F/q 结合使用，以计算均匀电场中带电粒子所受的力。

A charged particle moving through a potential difference V gains kinetic energy. For a particle of charge q and mass m, the speed gained by an electron or ion can be found by equating electric work to kinetic energy.

带电粒子经过电势差 V 后获得动能。对于电荷为 q、质量为 m 的粒子，电子或离子获得的速度可以通过将电场做功与动能相等来求出。

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