13. A cylinder is used as the Gaussian surface in computing the electric field for both an infinite line charge and an infinite plane of charge. Which of the following statements about this surface is false?
I. This surface honors the symmetry of the problem in both cases.
II. The flux through the ends of the cylinder is zero for the infinite line charge and nonzero for the infinite plane of charge.
III. The flux through the middle of the cylinder is nonzero for the infinite line charge and zero for the infinite plane of charge.
IV. The Gaussian surface is a real, hard surface for the infinite line charge, but not for the infinite plane of charge.