Q) Gauss' Law A. consider an infinitely long line of charge represented by the long line in the figure (the dashes indicate the line goes to infinity). Draw the electric field lines at each of the labeled points in the figure. B. In the figure below a cylindrical coordinate system has been superimposed on the line charge. The surface is oriented so that it bisects the line charge with the surface area vector parallel to the line charge, explain why the electric field can not depend on the angle variable t or the variable z, but can depend on r. C. Based upon these considerations if we want to use Gauss' law to determine the electric field due to this infinite line charge what kind of closed surface should we choose, and why? D. For a moment consider a finite line charge. Why would it be impossible to use Gauss' law to determine the electric field for a finite line charge? (Hint: consider what the electric field does near the ends of the charge distribution.) E. In the previous question you should have concluded that the correct Gaussian surface to use is a cylinder with the line charge running along the axis of the cylinder. Now use Gauss' law to determine the electric field from a line charge, with charge/unit length . Explain why the flux through the end-caps is zero, and argue that: JE . A = / EdA = EdA = EA, where A = 2act is the area of a cylindrical surface of radius r and height . Next determine Outin terms of A and L: Finally put it all together and find E(r)