Non-Conducting Sphere

Core Sentence / 核心句

A non-conducting sphere can hold charge distributed through its volume.

中文理解：非导体球可以让电荷分布在体积内部，常用体电荷密度描述。

For a uniformly charged solid sphere of radius $R$ :

E = \frac{k Q r}{R ^{3}} (r < R), E = \frac{k Q}{r ^{2}} (r \geq R)

Its electric potential is

V (r) = \frac{k Q}{2 R} (3 - \frac{r ^{2}}{R ^{2}}) (r < R), V (r) = \frac{k Q}{r} (r \geq R) .

看到 uniform volume charge、solid insulating sphere 或 inside/outside field 时使用。

不要套用导体内部 $E = 0$ ；内部 Gaussian surface 只包住 $Q (r) = Q r^{3} / R^{3}$ 。

AP电磁学第5次正课-电势差与电场电势关系 · sphere potential
- The interior potential requires a piecewise integral because the electric field changes at the surface.
AP电磁学第3次正课-高斯定律与对称带电体
- Uniform and nonuniform spherical volume-charge distributions are derived here.