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A Treatise on Electricity and Magnetism

James Clerk Maxwell

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THE WORD OF MOUTH

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DoctorOetker
severine is correct: it is in A Treatise on Electricity and Magnetism, which can be had free of charge from the Internet Archive. vol I https://archive.org/details/electricandmagne01maxwrich vol II https://archive.org/details/electricandmag02maxwrich The relevant section is in the preliminaries in Vol I : I assume you already know electromagnetism, I suggest jumping to pdf pages 52 "on potentials" and reading till 57. No modern textbook will explicitly introduce such an assumption, instead modern textbooks assume the student has been indoctrinated with cartesian product spaces i.e. R^3 etc. Such students would have seen in prior analysis courses that the line integral of the gradient of a scalar function does not depent on the path [... in R^n!]. So if curricula and students implicitly and a priori exclude spaces other than R^n, then no student will protest that for example the line integral of the electric field between 2 points could depend on the exact path, making all subsequent math and theorems more tractable, at the "small price" of a priori excluding the (arguably) confusing possibilities of handles (if you are a mathematiciann), wormholes (if your a physicist).…