1. 此时, Maxwell 方程组为 $$\beex \bea \Div{\bf D}&=\rho_f,\\ \rot {\bf E}&={\bf 0},\\ \Div{\bf B}&=0,\\ \rot{\bf H}&={\bf j}_f. \eea \eeex$$

2. 电荷守恒律方程: $$\bex \Div{\bf j}_f=0. \eex$$

3. 电势 $\phi$: $$\beex \bea &\quad {\bf E}=-\n\phi\\ &\ra {\bf j}_f=-\cfrac{1}{\gamma}\n\phi\quad\sex{Ohm\mbox{ 定律: }{\bf j}_f=\sigma {\bf E}=\cfrac{1}{\gamma}{\bf E}}\\ &=0=\Div{\bf j}_f=-\cfrac{\p}{\p x}\sex{\cfrac{1}{\gamma}\cfrac{\p\phi}{\p x}} -\cfrac{\p}{\p y}\sex{\cfrac{1}{\gamma}\cfrac{\p\phi}{\p y}} -\cfrac{\p}{\p z}\sex{\cfrac{1}{\gamma}\cfrac{\p\phi}{\p z}}. \eea \eeex$$

4. 边界条件: $$\bex \sez{{\bf E}}\times{\bf n}={\bf 0},\quad \sez{{\bf j}_f}\cdot{\bf n}=0 \eex$$ 化为电势 $\phi$ 满足的边界条件: $$\bex \sez{\phi}=0,\quad \sez{\cfrac{1}{\gamma}\cfrac{\p\phi}{\p n}}=0. \eex$$

5. 其他边界条件.