靜月庭: Maxwell's equations

真空中微分型

$\nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0}$

$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$

$\nabla \cdot \mathbf{B} = 0$

$\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t}\$

真空中積分型

$\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf E\;\cdot\mathrm{d}\mathbf A = \frac{Q(V)}{\varepsilon_0}$

$\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \frac {\partial \Phi_{B,S}}{\partial t}$

$\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf B\;\cdot\mathrm{d}\mathbf A = 0$

$\oint_{\partial S} \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \mu_0 I_S + \mu_0 \varepsilon_0 \frac {\partial \Phi_{E,S}}{\partial t}$

介質中微分型

$\nabla \cdot \mathbf{D} = \rho_f$

$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$

$\nabla \cdot \mathbf{B} = 0$

$\nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t}$

介質中積分型

$\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\;\cdot\mathrm{d}\mathbf A = Q_{f}(V)$

$\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \frac {\partial \Phi_{B,S}}{\partial t}$

$\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf B\;\cdot\mathrm{d}\mathbf A = 0$

$\oint_{\partial S} \mathbf{H} \cdot \mathrm{d}\mathbf{l} = I_{f,S} + \frac {\partial \Phi_{D,S}}{\partial t}$

輔助方程式

$\boldsymbol{D}=\varepsilon_0\boldsymbol{E}+\boldsymbol{P}=\varepsilon_r\varepsilon_0{\boldsymbol{E}}=\varepsilon{\mathbf{E}}$

$\boldsymbol{H}= \frac{ \boldsymbol {B}}{\mu_0} - \boldsymbol {M}=\frac{\boldsymbol{B}}{\mu_r\mu_0}=\frac{\boldsymbol{B}}{\mu}$

符號與單位

靜月庭