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sponsoredwalk

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It took me a quite a while to realize & accept that the derivations & variations of derivations in all the books basically reduce to applying a mish-mash of single, double, triple & surface integral techniques arbitrarily combined with the geometry of the situation arising & leaving in the derivations at random stages & that the kinds of geometric objects you can apply these techniques to are n-gons, conics, quadric surfaces let alone random portions, modifications (hollow, full etc...) & combinations of all of these (which is no small list when expanded out)...

Based on this little motivation, my question is: What other things in physics are there that once you encounter them you need to be able to calculate them for absolutely every geometric object I've mentioned? If it's not clear what I'm looking for, good answers could be: radius of gyration, gravitational field due to geometric objects, charge density of geometric objects containing charge, electric field due to geometric objects containing charge via Coulomb's Law, via Gauss law, electric potential due to geometric objects, hopefully you see what I mean...

Lest you think this an idle question, it's really functioning for me as a means to ensure I can deal with, & prepare for, certain aspects of advanced electromagnetism, quantum mechanics, statistical physics, classical & quantum field theory & be aware of the things that would hold me back in learning them. Had I been aware of this way of looking at things before I ever tried to learn electromagnetism I'd have breezed through the books, skipping these things has resulted in a sincerely painful headache of false knowledge & I never want to go through that again. I can't tell you how much I'd appreciate a helpful answer to this question so if you have a moment I'd be really greatful, thanks for your time