Maxwell's Equations

Topics

• Magnetic Charge

4 Laws

1. Gauss’s Law
2. Magnetic Monopole Law
3. Faraday’s Law
4. Ampere’s Law

Static Limit

$$\{\begin{array}{l}\nabla \times \vec{E}=0\\ \nabla \times \vec{B}={\mu }_0\vec{J}\\ \nabla \cdot \vec{E}=\frac{\rho }{{\epsilon }_0}\\ \nabla \cdot \vec{B}=0\end{array}$$

• When electromagnetic forces are static/unchanging

In Materials

$$\{\begin{array}{l}\nabla \times \vec{E}=-\frac{\partial \vec{B}}{\partial t}\\ \nabla \times \vec{H}=\overrightarrow{J_f}+\frac{\partial \vec{D}}{\partial t}\\ \nabla \cdot \vec{D}={\rho }_v\\ \nabla \cdot \vec{B}=0\end{array},\{\begin{array}{l}\vec{D}=ϵ\vec{E}\\ \vec{B}=\mu \vec{H}\\ \overrightarrow{J_f}=\sigma \vec{E}\end{array}$$