In my textbook there are two types of electric flux problems: 1. Find the electric flux through the parabolodial surface due to a uniform electric field of magnitude E_0 in the direction as shown. Here they use ##\pi r^2 * E = \Phi ## 2. An infinitely long line charge having a uniform charge per unit length ##\laambda ## lies a distance d from point O. construct a sphere with center O, and radius less than d. Find the flux thru the surface of the sphere. Here the answer is 0 since q enclosed is 0. But for #1, wouldn't it be zero also since the paraboloid has no charge contained inside of it?