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A ring in a magnetic field: (a) in the normal state; (b) in the superconducting state (Meissner effect pushes external fields out; (c) after the external field is removed. In regard to our last question -the spatial extent of such magnetic fields -I cannot help thinking of yet another of H.A. Lorentz's remarks -one he made at the occasion of the 1921 Solvay Conference, while discussing the ring current model of an electron: "The idea of a rotating ring [in French: anneau tournant] has a great advantage when trying to explain some issues [in the theory of an electron]: it would not emit any electromagnetic radiation. It would only produce a magnetic field in the immediate space that surrounds it. [...]" (H.A. Lorentz, 1921 Solvay Conference, boldface and italics added)

A ring in a magnetic field: (a) in the normal state; (b) in the superconducting state (Meissner effect pushes external fields out; (c) after the external field is removed. In regard to our last question -the spatial extent of such magnetic fields -I cannot help thinking of yet another of H.A. Lorentz's remarks -one he made at the occasion of the 1921 Solvay Conference, while discussing the ring current model of an electron: "The idea of a rotating ring [in French: anneau tournant] has a great advantage when trying to explain some issues [in the theory of an electron]: it would not emit any electromagnetic radiation. It would only produce a magnetic field in the immediate space that surrounds it. [...]" (H.A. Lorentz, 1921 Solvay Conference, boldface and italics added)

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This paper explores the common concept of a field and the quantization of fields. We do so by discussing the quantization of traveling fields using our photon model, and we also look at the quantization of fields in the context of a perpetual ring current in a superconductor. We then relate the discussion to the use of the (scalar and vector) poten...