Maxwell's Equations for different Medium

In the later half of the nineteenth century, Maxwell demonstrated that all previously established experimental facts regarding electric and magnetic fields could be summed up in just four equations. Nowadays these equations are generally known as Maxwell’s equation. Maxwell did not proved the equations. He only gave above opinion and some mathematical verification and modification of others. These equations can be represented as integral and differential form.

Let’s go

Here, 

H= magnetic field strength

E= electric field intensity

J= conduction current density

D= electric flux density

B= magnetic flux density

ρ_v = volume charge density

dL is the differential length and dS is the differential area whose direction is always outward normal to the surface.

When the field are static all field terms which have time derivatives  become zero, that is:

   dB/dt = 0

  dD/ dt = 0

So the Maxwell’s equation’s for static fields become:

 

Now we know the characteristics of free space that:

Relative permittivity ϵ_r = 1

Relative permeability µ_r = 1

Conductivity σ = 0

Conduction current density J = 0

Volume charge density ρ_v = 0

Characteristics impedance = 377Ω or 120π

So the Maxwell’s equation’s for the free space but no static field become

    Differential form                   Integral from

                              

Also the Maxwell’s equation’s for the free space with static field become: