Calculating E Field Inside Cylinder of Finite Height

[Fibo112]

I have a cylinder with radius r and height h and a uniform charge density. Now I am supposed to calculate the E field inside the cylinder. If the cylinder was infinitely long the symmetry would dictate that the field can only point radially outward, so gausses law would give me a field of zero everywhere. In the solutions it uses the argument that the field only depends on the radius due to symmetry. But in this case the cylinder is not infinite, so why can't the field depend on the height?

 

[Dale]

I have a cylinder with radius r and height h and a uniform charge density. Now I am supposed to calculate the E field inside the cylinder. If the cylinder was infinitely long the symmetry would dictate that the field can only point radially outward, so gausses law would give me a field of zero everywhere. In the solutions it uses the argument that the field only depends on the radius due to symmetry. But in this case the cylinder is not infinite, so why can't the field depend on the height?

It can depend on height. In this case it can not depend on the angular coordinate.