A thin straight infinitely long conducting wire having charge density λ is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.



The thin infinitely long straight line has a linear charge density λ. Since the electric field for this kind of configuration will be radial and perpendicular to the wire, there will be no flux through the flat surfaces of the cylinder. Also, the electric field (E) will be constant at every point on the curved surface of the cylinder (as all points on it are equidistant from the wire) and perpendicular to it. We shall us Gauss's law to find the electric flux through the cylinder. The charge enclosed by the cylinder is λ × l, as l is the length of the cylinder and it is also the length of the charged wire within the cylinder. φ = λl / ε0