MathLiveMaxwell's equations (integral form)
The four Maxwell equations written over closed curves, surfaces and volumes, relating electric and magnetic fields to charges and currents. They are used to describe classical electromagnetism without assuming any particular coordinate system or differentiability of the fields.
\begin{aligned} \oint_{\partial S} \mathbf{E}\cdot d\mathbf{l} &= -\frac{d}{dt}\int_S \mathbf{B}\cdot d\mathbf{S} \\ \oint_{\partial V} \mathbf{B}\cdot d\mathbf{S} &= 0 \\ \oint_{\partial V} \mathbf{D}\cdot d\mathbf{S} &= \int_V \rho\,dV \\ \oint_{\partial S} \mathbf{H}\cdot d\mathbf{l} &= \int_S \left(\mathbf{J}+\frac{\partial \mathbf{D}}{\partial t}\right)\cdot d\mathbf{S} \end{aligned}What the symbols mean
| electric field (V/m) | |
| magnetic flux density (T) | |
| electric displacement field (C/m^2) | |
| magnetic field strength (A/m) | |
| free electric charge density (C/m^3) | |
| free current density (A/m^2) | |
| open surface bounded by the curve \partial S | |
| volume bounded by the closed surface \partial V | |
| line element along the curve | |
| oriented surface element | |
| time |
About this formula
- FieldPhysics
- TopicElectromagnetism
- LevelUniversity
- Also calledmaxwell equations, faraday law integral, gauss law electric integral, gauss law magnetism, ampere maxwell law integral, electromagnetism equations integral
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