Conducting Sphere

Core Sentence / 核心句

A conducting sphere has mobile charges that redistribute to electrostatic equilibrium.

中文理解：导体球静电平衡时电荷在表面重新分布，内部电场常为 0。

Formula / 公式或规则

For a conducting sphere of radius $R$ in electrostatic equilibrium:

$$E=0(r<R),E=\frac{kQ}{r^2}(r\ge R)$$ $$V=\frac{kQ}{R}(r\le R),V=\frac{kQ}{r}(r\ge R)$$

When To Use / 什么时候用

看到 charged conductor、electrostatic equilibrium、inside/outside field 或 spherical symmetry 时使用。

Watch Out / 易错点

内部 $E=0$ 是 electrostatic equilibrium 的结论；球外才可等效为球心点电荷。

Search and Source Mentions / 搜索与出现位置

Mentioned In / 出现位置

• AP电磁学第6次正课-等势面与静电平衡 · conducting-sphere potential
  • “A conducting sphere has constant potential throughout its interior.”
• AP电磁学第1次正课-电荷库仑定律与电场 · Supplement 12: What Not to Add Yet / 暂时不补进本节课的内容
  • - Non-Conducting Sphere

Connected Notes / 连接

• AP电磁学第3次正课-高斯定律与对称带电体

• Conductors

• Gauss’s Law

• AP电磁学第6次正课-等势面与静电平衡

• Electrostatic Equilibrium

• Equipotential Surface