1. Gauss Law:

The equation describes the generation and distribution of electric field, and its mathematical expression is: ∮ e da = ε 0 * ∫ ρ dv. Where ∮ e da represents the flux of the electric field vector e on the closed surface, ε0 represents the vacuum dielectric constant, ρ represents the charge density in the closed surface, and ρ dv represents the volume fraction of the charge density in the closed surface.

2. Gauss magnetic law:

The equation describes the generation and distribution of magnetic field, and its mathematical expression is: ∮ b da = 0. Where ∮ b da represents the flux of magnetic field vector b on the closed surface, and there is no magnetic charge on the closed surface.

3. Faraday's law of electromagnetic induction:

The equation describes the influence of magnetic field on the generation and change of electric field, and its mathematical expression is ∮ e DL =-d (∫ b Da)/dt. Where ∮e D 1 represents the line integration of electric field vector e along the closed loop, ∫ b da represents the flux of magnetic field vector b through the closed surface, and t is time.

4. Ampere loop law:

The equation describes the influence of current on the generation and change of magnetic field, and its mathematical expression is ∮ B DL = μ 0 * (∫ J DA+ε 0 * D (∫ E DA)/dt). Where ∮ b dl represents the line integral of magnetic field vector b along the closed loop, μ0 represents the magnetic permeability of vacuum, ∫ j da represents the area fraction of current density vector j passing through the closed surface, ∫ e da represents the flux of electric field vector e passing through the closed surface, and t represents time.

These four basic equations describe the generation, propagation and interaction of electromagnetic fields and are the basis of electromagnetism.