Gauss's law provides a relatively easy way to find E-fields for charged spheres, long sticks or cylinders, and large plates. The last two, of course, are approximations in the end, but ends, edges, and corners really make for a difficult math problem. When stuck with such a problem, we have no choice but to stick (heh, heh) with the fundamentals. That is, point charges. We know how to handle point charges, and physically that is all a charged object is - a bunch of extra charged particles. So we need to set up an integral and add up a bunch of small fields or potentials! Check it out.