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Electric Fields — 考纲逐点解读

18.1 Electric fields and field lines​

1. Understand that an electric field is an example of a field of force and define electric field as force per unit positive charge​

  • Electric field: 电荷周围空间存在的一种力场
  • Electric field strength EE: E=FqE = \frac{F}{q} 单位：N C−1^{-1} 或 V m−1^{-1}

2. Recall and use F=qEF = qE for the force on a charge in an electric field​

  • 正电荷受力方向与 EE 相同，负电荷相反

3. Represent an electric field by means of field lines​

  • 电场线方向：从正电荷指向负电荷
  • 电场线密度表示场强大小（越密场越强）
  • 电场线不相交
  • 垂直于导体表面
  • Radial field: 点电荷周围，电场线从电荷向外辐射（正）或向内汇聚（负）
  • Uniform field: 平行板之间，电场线平行等距

18.2 Uniform electric fields​

1. Recall and use E=ΔV/ΔdE = \Delta V / \Delta d to calculate the field strength of the uniform field between charged parallel plates​

  • 对平行板间的匀强电场： E=VdE = \frac{V}{d} 其中 VV 是板间电势差（p.d.），dd 是板间距

2. Describe the effect of a uniform electric field on the motion of charged particles​

  • 正电荷沿电场方向加速，负电荷相反
  • 运动分析：
    • 沿 EE 方向：F=qEF = qE，a=qE/ma = qE/m
    • 垂直 EE 方向：速度不变
    • 轨迹：抛物线（类似抛体运动）

18.3 Electric force between point charges​

1. Understand that for a point outside a spherical conductor, the charge on the sphere may be considered to be a point charge at its centre​

  • 球形导体外部的电场等同于全部电荷集中在球心的点电荷

2. Recall and use Coulomb's law F=Q1Q2/(4πϵ0r2)F = Q_1 Q_2 / (4\pi \epsilon_0 r^2) for the force between two point charges in free space​

  • F=14πϵ0Q1Q2r2F = \frac{1}{4\pi \epsilon_0} \frac{Q_1 Q_2}{r^2}
  • 14πϵ0=8.99×109\frac{1}{4\pi \epsilon_0} = 8.99 \times 10^9 m F−1^{-1}
  • 同号电荷：斥力（F>0F > 0）；异号电荷：引力（F<0F < 0）

18.4 Electric field of a point charge​

1. Recall and use E=Q/(4πϵ0r2)E = Q / (4\pi \epsilon_0 r^2) for the electric field strength due to a point charge in free space​

  • 方向：正电荷向外，负电荷向内
  • 与 r2r^2 成反比

18.5 Electric potential​

1. Define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to the point​

  • V=WqV = \frac{W}{q}
  • 参考点：无穷远处 V=0V = 0
  • 单位：V（volt）= J C−1^{-1}

2. Recall and use the fact that the electric field at a point is equal to the negative of potential gradient at that point​

  • E=−dVdrE = -\frac{dV}{dr}
  • 在匀强电场中：E=ΔVΔdE = \frac{\Delta V}{\Delta d}
  • 负号表示电场指向电势降低的方向

3. Use V=Q/(4πϵ0r)V = Q / (4\pi \epsilon_0 r) for the electric potential in the field due to a point charge​

  • 正点电荷周围 V>0V > 0，负点电荷周围 V<0V < 0
  • 与 rr 成反比（不是 r2r^2）

4. Understand how the concept of electric potential leads to the electric potential energy of two point charges and use EP=Qq/(4πϵ0r)E_P = Qq / (4\pi \epsilon_0 r)​

  • 电势能：EP=qV=Qq4πϵ0rE_P = qV = \frac{Qq}{4\pi \epsilon_0 r}
  • 同号电荷：EP>0E_P > 0（排斥，分离时释放能量）
  • 异号电荷：EP<0E_P < 0（吸引，束缚态）