Electric Fields

考纲要求

• 18.1 Electric fields and field lines
  • Define electric field as force per unit positive charge
  • Use $F = qE$
  • Represent field by field lines
• 18.2 Uniform electric fields
  • Use $E = \Delta V / \Delta d$ for parallel plates
  • Describe effect on charged particles
• 18.3 Electric force between point charges
  • Coulomb's law: $F = Q_1 Q_2 / (4\pi \epsilon_0 r^2)$
• 18.4 Electric field of a point charge
  • $E = Q / (4\pi \epsilon_0 r^2)$
• 18.5 Electric potential
  • Define: work done per unit positive charge from infinity
  • $E = -dV/dr$ (potential gradient)
  • $V = Q / (4\pi \epsilon_0 r)$
  • $E_P = Qq / (4\pi \epsilon_0 r)$

常见题型

• 定义题：Define electric field strength / electric potential
• 计算题：Coulomb's law / field strength / potential
• 作图题：Sketch field lines / $E$-$r$ / $V$-$r$ graphs
• 解释题：Compare electric and gravitational fields / Explain motion of charged particles

核心公式

$F = qE$

$E = \frac{\Delta V}{\Delta d}$

$F = \frac{Q_1 Q_2}{4\pi \epsilon_0 r^2}$

$E = \frac{Q}{4\pi \epsilon_0 r^2}$

$V = \frac{Q}{4\pi \epsilon_0 r}$

$E_P = \frac{Qq}{4\pi \epsilon_0 r}$

常见错误

• 电场强度 $E$ 是矢量，电势 $V$ 是标量
• Coulomb's law 忘记分母中的 $4\pi \epsilon_0$
• 点电荷外部的 $E$ 和 $V$ 公式中的 $r$ 是从电荷中心算起
• $E = -\frac{dV}{dr}$ 的负号表示电场指向电势降低方向