Assume that the linear charge density is the same for the charged infinite cylinder and the infinite line. By Gauss' Law, I know the charge enclosed is the same given a Gaussian cylinder of a certain length and so the E fields must be the same at any given distance from the axis of symmetry for both objects, given that the distance is greater than the radius of the cylinder.
I just don't understand intuitively why this is the case. For a charged infinite cylinder, since the charges are distributed only on the surface of the cylinder, shouldn't the E field produced by the cylinder at a distance r > a (a being the radius of the cylinder) from the axis of symmetry of the cylinder be greater in magnitude than that produced by an infinite line of charge at the same radius r?
Best Answer
Maybe it helps to compare your cylinder with a cylinder with a tiny radius, but with the same linear charge density. To have the same linear charge density, the smaller cylinder has to have a large surface density, because its surface per unit length is smaller.