Consider an infinitely long thin wire with uniform linear charge density λ. That is, the charge per unit length is λ and this assumed to be the same for all points on the wire. From considerations of symmetry, we can say that the electric field is radially directed. The magnitude of the electric field is same at all those points which are equidistant from the wire. Let us find the electric field intensity at any point P at a perpendicular distance r from the axis of the wire. A cylinder of radius r and arbitrary length l coaxial with the axis of the wire is chosen as the Gaussian surface.Since the Gaussian surface is a closed surface, this cylinder is closed at each end by plane caps normal to the axis. The magnitude of is constant at all points on the surface of the cylinder, as those points are equidistant for the wire and is normal to the surface (outward).