How to do a NON-Gauss's law problem - A Partial Ring of Charge

Here is another example of a NON-Guass's law problem, a partial ring of charge. This is a combination of sticks and rings, the two classic cases where we might have to calculate something like an E-field or potential on some axis. In any case like this, we need to use the fundamentals: point charges, which we know how to do exactly. We break the problem into a bunch of little charges, find the small contribution, and then add them all up using an integral! Let's check it out, and I hope it helps.

How to do NON-Guass's Law Problem - A Stick WITH Ends

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.