Let's begin by understanding the principles at work here. Electric flux relates the field to the total number of electric field lines passing through a given area. When the electric field is perpendicular to an area (as it is in this case, given the field is vertical and the area is horizontal), their dot product simplifies to the product of their magnitudes. Here, the electric field emulates from the top and bottom of the cylinder that each contain an area of 1 square meter.
Firstly, note that the electric field strength is given as 2.10 x 10^3 N/C. This is an intensive property which is independent of the amount of material or the size of the sample. In this case, it means that the force that a unit positive electric charge would experience if placed in the field.
Next, take into consideration the size of the cylinder. For simplicity's sake, we're working with a cylinder each of whose top and bottom faces has an area of 1 m^2.
Because the electric field is perpendicular to the top and bottom surface of the cylinder, to calculate the electric flux, you simply multiply the magnitude of the electric field by the total area through which the field lines pass. Given that the magnitude of the field is 2.10 x 10^3 N/C and the total area of the cylinder's top and bottom is 2 m^2, this means:
Electric flux = Electric field strength x Total area
Electric flux = 2.10 x 10^3 N/C x 1 m^2
Electric flux = 2.10 x 10^3 (N.m^2)/C
Therefore, the electric flux through the cylinder's top and bottom surfaces is 2.10 x 10^3 (N.m^2)/C.
This tells us how a field interacts with the area of a surface, which is important in understanding and measuring fields and their effects.