Maxwell Equations

Maxwell equations describe the behaviour of the magnetic field and electric field.

$$\{\begin{array}{cccc}\nabla \cdot E& =& \frac{\rho }{{ϵ}_0}& \text{Gauss’ law}\\ \nabla \cdot B& =& 0& \text{Gauss’ law for magnetism}\\ \nabla \times E& =& -{\partial }_{t}B& \text{Faraday’s law of induction}\\ \nabla \times B& =& {\mu }_0(J+{ϵ}_0{\partial }_{t}E)& \text{Ampere’s circuital law}\end{array}$$

In the above,

• $E$ is the electric field
• $B$ is the magnetic field
• $J$ is the current density
• $\rho$ is the electric charge
• ${ϵ}_0$ is the vacuum permittivity
• ${\mu }_0$ is the vacuum permeability
• $\nabla \cdot$ is the Divergence
• $\nabla \times$ is the Curl

I don’t yet know the intuitive meaning behind each equation. Help me ❓