Electromagnetic quantities in a non-polarized medium

The equations of relativistic mechanics cannot easily be extended to continuous media (also known as continua). Indeed, in this case, we need to switch from looking at the material particle - a molecule, an electron or an ion, to looking at the ensemble formed by a very large number of particles, upon which we need to perform statistical calculations. Necessarily, therefore, we need to find the definition of a coherent relativistic thermod5mamics if we wish to correctly describe the motion of the continuum. These problems are highly complex. 

On the other hand, unlike the study of sets of particles, the study of an electromagnetic field is much easier, particidarly when we are dealing with non-polarized media. Thus, we shall begin by looking at fields in the absence of polarization. 

In a medium - be it polarized or otherwise — it is possible to define a current 4-vector. In order to do so, we introduce a scalar pQ, which is the electrical charge per unit volume. 

The conservation of electricity expresses the fact that the integral of the charge flux 4/ over an enclosed surface 45 = 9(4V) is null  

With the divergence theorem, because of the conditions of continuity of the quantities, we can deduce that  

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