MathLiveMaxwell's equations
These four partial differential equations describe how electric and magnetic fields are produced by charges and currents and how they change in time and influence each other. They form the foundation of classical electromagnetism and are used throughout electrical engineering and physics.
\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\left(\mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}\right) \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) |
About this formula
- FieldPhysics
- TopicElectromagnetism
- LevelUniversity
- Also calledMaxwell's laws, electromagnetism equations, differential form of Maxwell's equations, Gauss's law for electricity and magnetism, Faraday's law and Ampère-Maxwell law, classical electromagnetism
- SourceWikidata Q51501
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