I'm confused with the Gauss' Law to calculate the electric field for two coaxial cylindrical conductors of finite length.
I know that we can use the Gauss' Law to calculate the electric field for two coaxial cylindrical conductors of INFINITE length, but I don't see why we can use the Gauss' Law for the one of finite length.
Ok here is the problem.
Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius a = 2 cm, length L = 10 m and carries a total charge of Qinner = + 8 nC (1 nC = 10-9 C). The outer cylinder has an inner radius b = 6 cm, outer radius c = 7 cm, length L = 10 m and carries a total charge of Qouter = - 16 nC (1 nC = 10-9 C). What is Ex, the x-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance r = 4 cm from the origin and makes an angle of 30o with the x-axis?
The problem I have is that, I thought, in order to use the Gauss' law, the electric field has to be constant through out a gaussian surface, but I don't see why we can use a cylindrical shell of radius $4cm$ and length $10m$ to calculate the electric field at $P$ since I think the elctric field is not the same if I move from $0m$ to $10m$ on z-axis. Help me.