I'm a little disappointed in myself for not being able to calculate this or find the answer online, but I've hit a bit of a mental block so I was hoping someone could help me out a bit. I was doing a thought experiment involving kerr-newmann black holes, and basically I would like to calculate what the mass of a charged, spinning ring would be CLASSICALLY. So lets say there is a ring of radius r, charge density λ, and angular velocity ω. How much work would it take to construct such a ring? A more simple question, that I'm struggling with as well (not proud of myself here) is just to find the work required to shrink an infinitely large charged ring to radius r. The answer I get is infinite but I find that very hard to believe...
Hi, I think for your second question you are right. It blows up, but its an artifact of assuming that the wire is infinitely tiny. See for interesting discussion: http://physics.stackexchange.com/questions/16520/potential-energy-of-a-charged-ring http://physics.stackexchange.com/questions/9830/tension-in-a-curved-charged-wire-electrostatic-force-does-wire-thickness-mat