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There appears to be some infinities in classical electromagnetism:

The total energy contained in the electric field of a point charge diverges.
The potential at a point charge diverges.
The potential at a line charge diverges.
The potential at a volume charge does not diverge.

Are there any references/discussions providing rigorous arguments to show these, and other similar phenomena?

I found a few rather informal explanations:

Curvature argument

Green's function

From StackExchange:

The problem of infinite energy of electron as point charge?

Electromagnetism for mathematicians

Mathematical book on "Maxwell" equation

Cheng
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  • There are infinities in laws like F=GMm/r^2 as well, the gravitational force is infinite at zero distance. However in practice, this don't usually cause issues, because we tend to double check with reasoning when solving a calculation, or code in some checks (eg. r can never be less than 10), and the formula gives what we need to predict things. When the answers don't make sense, we look inside and can usually find the problem (eg they have collided). – James Dec 05 '22 at 11:01
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    Maybe they are better called singularities then.... – Cheng Dec 05 '22 at 11:21
  • Maybe a mathematically rigorous discussion on singularites in field theory/potential theory(?) works just as well – Cheng Dec 05 '22 at 11:47

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