Electric Field Strength | 电场强度

📚 Electric Field Strength | 电场强度

An electric field describes how a charged object influences the space around it. A stationary charged particle placed in this region experiences an electric force. At A Level, we focus on electric fields produced by point charges and by charged parallel plates, and we use electric field strength to measure how strong the field is at a specific point.

电场描述带电物体如何影响其周围空间。放置在该区域中的静止带电粒子会受到电场力。在 A Level 课程中，我们主要研究点电荷和带电平行板产生的电场，并用电场强度来衡量某一点处电场的强弱。

1. What is an Electric Field? | 什么是电场？

An electric field is a region of space in which a charged object experiences an electric force. The field is created by other charges or by changing magnetic fields. The direction of the field at a point is defined as the direction of the force on a small positive test charge placed there.

电场是空间中的一个区域，位于其中的带电物体受到电场力。电场由其他电荷或变化的磁场产生。电场中某点的方向定义为放在该点的小正检验电荷所受力的方向。

2. Defining Electric Field Strength | 电场强度的定义

The electric field strength E at a point is defined as the force per unit positive charge placed at that point. If a small positive test charge q experiences a force F, then E = F/q. Since E is a vector, its direction is the same as the direction of the force on a positive test charge. The test charge must be small enough that it does not significantly disturb the source charges.

电场强度 E 定义为放置在某点的单位正电荷所受的电场力。如果一个小正检验电荷 q 在电场中受力为 F，那么 E = F/q。E 是矢量，其方向与正检验电荷所受力的方向相同。检验电荷必须足够小，以免明显改变源电荷分布。

E = F / q

3. Units of Electric Field Strength | 电场强度的单位

The SI unit of electric field strength is newton per coulomb, written N C⁻¹. Because potential difference is work done per unit charge, and work divided by distance is force, the equivalent unit is volt per metre, V m⁻¹. Therefore 1 N C⁻¹ = 1 V m⁻¹. In exam questions, either unit is acceptable unless the question specifies otherwise.

电场强度的国际单位是牛顿每库仑，写作 N C⁻¹。由于电势差等于每单位电荷的电功，而功除以距离等于力，因此等价单位是伏特每米，V m⁻¹。因此 1 N C⁻¹ = 1 V m⁻¹。在考试中，除非题目另有规定，两种单位均可使用。

4. Field of a Point Charge | 点电荷的电场

For an isolated point charge Q, Coulomb’s law states that the force on a small test charge q at distance r is F = Qq/(4πε₀r²), where ε₀ is the permittivity of free space. Dividing by q gives the electric field strength due to the point charge: E = Q/(4πε₀r²). This field is radial and obeys an inverse-square law. The field points radially outward for a positive Q and radially inward for a negative Q.

对于孤立的点电荷 Q，库仑定律表明距离 r 处的小检验电荷 q 所受的力为 F = Qq/(4πε₀r²)，其中 ε₀ 是真空介电常数。除以 q 得到点电荷产生的电场强度：E = Q/(4πε₀r²)。该电场呈辐射状，遵循平方反比定律。Q 为正时电场沿径向向外，Q 为负时沿径向向内。

E = Q / (4πε₀ r²)

5. Uniform Electric Fields between Parallel Plates | 平行板间的匀强电场

Between two oppositely charged parallel plates, the electric field is uniform in the central region, far from the plate edges. Field lines are straight, parallel and equally spaced, indicating that both the magnitude and direction of E are constant. This uniform field is very useful for deflecting charged particles and for investigating the relationship between potential difference and field strength.

在两块带异种电荷的平行板之间，远离板边缘的中央区域电场是均匀的。电场线为直线、平行且等间距，表明 E 的大小和方向均保持不变。这种匀强电场在偏转带电粒子以及研究电势差与电场强度的关系时非常有用。

6. Relationship E = V/d | E = V/d 关系

If the potential difference between the plates is V and the plate separation is d, then the electric field strength is E = V/d. To derive this, consider moving a positive charge q from one plate to the other through the potential difference V. The work done is W = qV. In a uniform field, the force is constant, so W = F d = q E d. Equating the two expressions gives qV = q E d, hence E = V/d. This equation applies only to uniform fields.

若两极板间电势差为

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