What is the potential error in the proof of no magnetic fields?

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SUMMARY

The discussion centers on the potential error in the proof of the absence of magnetic fields as presented in question #33 of a specific book. The primary focus is on the statement B=curl(grad(u)) = 0, which participants suggest may be dimensionally incompatible. Additionally, the application of the divergence theorem is questioned, particularly regarding its use on closed surfaces without boundaries that would allow for invoking Stokes' theorem. These insights highlight critical considerations in electromagnetic theory.

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  • Understanding of vector calculus, particularly curl and gradient operations.
  • Familiarity with electromagnetic theory, specifically Maxwell's equations.
  • Knowledge of the divergence theorem and Stokes' theorem.
  • Experience with mathematical proofs in physics contexts.
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  • Study the implications of the divergence theorem in electromagnetic contexts.
  • Explore the relationship between curl and gradient in vector calculus.
  • Review the application of Stokes' theorem in closed surfaces.
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Physicists, mathematicians, and students studying electromagnetic theory or vector calculus who seek to deepen their understanding of the mathematical foundations of magnetic fields.

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hi kevi55

had a very quick look... could it be something like divergence theorem is for a closed surface so doesn't have a boundary to invoke stokes theorem on?
 

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