MathLiveMaxwell's equations (differential form)
The four local equations of classical electromagnetism in vacuum form (using vacuum permittivity and permeability), relating electric and magnetic fields to their sources, charge density and current density. They describe how electromagnetic fields are generated and how they propagate. In media, the form written with D and H is used instead.
\begin{aligned}\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned}What the symbols mean
| electric field (V/m) | |
| magnetic flux density (T) | |
| electric charge density (C/m^3) | |
| electric current density (A/m^2) | |
| vacuum permittivity (F/m) | |
| vacuum permeability (H/m) | |
| time (s) | |
| del operator (spatial gradient vector) |
About this formula
- FieldPhysics
- TopicElectromagnetism
- LevelUniversity
- Also calledMaxwell equations, differential form of Maxwell equations, Gauss law electric and magnetic, Faraday law curl E, Ampere-Maxwell law, classical electromagnetism equations
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