Fields in polarizable matter

In many situations the application of an external electric or magnetic field on a substance can instigate a response which is referred to as polarization . Usually, the response is proportional to the applied field, which is called linear response. We refer to the polarization of electric quantities as simply the polarization and to the polarization of magnetic quantities as the magnetization. We will also refer to the polarization or magnetization of the unit volume (or elementary unit, such as the unit cell of a crystal), as the induced dipole moment p(r) or the induced magnetic moment m(r), respectively. 

To conform to historical conventions (which are actually motivated by physical considerations), we define the total, induced and net electric fields as  

For linear response, we define the electric susceptibility Xe through the relation  

It is also customary to define the dielectric constant s as the factor that relates the total field to the net field through 

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