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It seems every time one of my pages gets vandalized and reverted, I see room for improvement. Keep up the good work, Billclintonlover!
! Name
! Name
! differential form
! differential form
! differential form, E and B only
! integral form
! integral form
|-
|-
| Coulomb's law of electrostatics, or [[Gauss's Law]]:
| Coulomb's law of electrostatics, or [[Gauss's Law]]:
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\nabla \cdot \mathbf{D} = \rho</math>
| <math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
| <math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
|-
|-
| Absence of magnetic monopoles:
| Absence of magnetic monopoles:
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\nabla \cdot \mathbf{B} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
| <math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
|-
|-
| Faraday's Law of Induction:
| Faraday's Law of Induction:
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
| <math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
|-
|-
| Ampère's Law, or the Biot-Savart Law, plus displacement current:
| Ampère's Law, or the Biot-Savart Law,
:plus displacement current:
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>
| <math>\nabla \times \mathbf{B} = \mu \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}} {\partial t}</math>
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
| <math>\oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} +
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
\int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>