Faraday's criterion (The magnitude of Electric field is proportional to the number of field lines) According to Halliday et al, the magnitude of Electric field is proportional to the number of lines per unit area perpendicular to the field.
My book (Halliday et al) states that this criterion, called Faraday's criterion, is helpful to draw field lines in a space region, but I can't understand why the area must be proportional to the electric field.
In my opinion, I think it is important because if the area is not perpendicular to the field, it is impossibile to collect all the field lines on the surface.
Then I want to know if this criterion is valid only if the magnitude of electric field is constant everywhere on the surface or not. 
If I assume there is an electric field in a space region with magnitude and direction which are not the same for each point, how do I apply this criterion?
I hope someone can help me. I feel discouraged by now and I would like to learn more. 
 A: Without further explanation, the statement that fields are proportional to the number of field lines crossing a perpendicular surface is nonsense, because for each point of the space there is a field line. Therefore, independently on the intensity of the field, one would count an infinite number of points and of field lines. 
The necessary specification which is needed to provide meaning to that statement is that, when drawing field lines, it is necessary to choose a finite number of field lines. If one starts choosing a finite number of equally spaced points on a surface where the field has the same intensity (in symmetric cases, on a planar section of the surface, for 2D drawings), field equations will rule how the chosen lines will be continued in the space. 
In the whole space where the field is solenoidal (its divergence is zero, which is the case of magnetic field and electric field in regions without charges) we can choose a  flux tube i.e. a volume made by two surfaces locally orthogonal to the field and a lateral surface coinciding with field lines. The flux through such a volume is zero, as well as the flux through the lateral surface and, as a consequence, the fluxes through the two orthogonal surfaces have the same absolute value (conservation of flux along flux tubes). Therefore, the largest is the surface, the smallest the field. If only a finite number of lines has been drawn, the number of lines per unit area of an orthogonal surface will be  proportional to the field intensity.
That is the reason for such a drawing recipe. It  provides a simple way to estimate space variations of field intensity by visual inspection of a good drawing of field lines.
A: I'm not sure about the term "Faraday's criterion", but what is being referred to here is field line density. Density (in this context) is something that occurs at a given point in space and can certainly vary over an area or volume. Technically it does not refer to some trait of a given volume or area. If we casually say a given volume or area has a certain density, we only mean that that is the density on average over that volume or area. A "unit area" is mentioned here only to convey the concept of density, because density is in lines per unit area. Of course, if a field varies over a given area, we must be careful to note that.
