Maxwell's Equations

When learning the University Physics, the chapter of Maxwell's Equations was jumped over. Now, in the Electromagnetic Field and Electromagnetic Waves, that's an important role, and how beautiful the formulas are, which like poems.

Integral Form

\[ \begin{aligned} \oint_{C} \boldsymbol{H} \cdot \mathrm{d} \boldsymbol{l}&=\int_{S} \boldsymbol{J} \cdot \mathrm{d} \boldsymbol{S}+\int_{S} \frac{\partial \boldsymbol{D}}{\partial t} \cdot \mathrm{d} \boldsymbol{S}\\ \oint_{C} \boldsymbol{E} \cdot \mathrm{d} \boldsymbol{l}&=-\int_{S} \frac{\partial \boldsymbol{B}}{\partial t} \cdot \mathrm{d} \boldsymbol{S}\\ \oint_{S} \boldsymbol{B} \cdot \mathrm{d} \boldsymbol{S}&=0\\ \oint_{S} \boldsymbol{D} \cdot \mathrm{d} \boldsymbol{S}&=\int_{V} \rho \mathrm{d} V \end{aligned} \]

Differential Form

\[ \begin{aligned} \nabla \times \boldsymbol{H}&=\boldsymbol{J}+\frac{\partial \boldsymbol{D}}{\partial t} \\ \nabla \times \boldsymbol{E}&=-\frac{\partial \boldsymbol{B}}{\partial t} \\ \nabla \cdot \boldsymbol{B}&=0 \\ \nabla \cdot \boldsymbol{D}&=\rho \end{aligned} \]