ABSTRACT
An example of a nonlinear behavior in the quasi-static domain is the nonlinear permeability of ferromagnetic materials.
To be more specic and restricting for the moment to the electric case, the electric polarization P that usually is written as
P = εoχ:E, (8.1)
where εo is vacuum permittivity, χ is called electric susceptibility and usually is a tensor of rank 2 with no dimension, and E is the electric eld vector, in the general case takes the form
P = f(E), (8.2)
where f(E) is a function depending in the considered material. In many cases, Equation 8.2 may be expanded as a function of the dierent powers of E, as
P = εoχE + χ(2):E ⋅ E + χ(3):E ⋅ E ⋅ E + …, (8.3)
where χ(2), χ(3), and so on are called susceptibility of second, third, … order and are tensors.
