JOURNAL ARTICLE

Recovering seldom-used theorems of vector calculus and their application to problems of electromagnetism.

  • Published In: American Journal of Physics, 2024, v. 92, n. 5. P. 354 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Pérez-Garrido, A. 3 of 3

Abstract

This article focuses on proving several integral vector calculus theorems using differential forms, including two identities not previously published, and demonstrates their applications in electromagnetism. The theorems, expressed in equations (3)–(6), extend beyond commonly known results like Gauss's and Stokes's theorems, providing new integral identities involving scalar and vector fields. Applying these identities, the paper derives general expressions for the net magnetic force and torque on current-carrying loops in both uniform and nonuniform magnetic fields, offering insights that differ from standard textbook treatments. These results highlight the utility of differential forms in revealing subtle physical effects and enhancing the theoretical understanding of electromagnetic phenomena.

Additional Information

  • Source:American Journal of Physics. 2024/05, Vol. 92, Issue 5, p354
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2024
  • ISSN:0002-9505
  • DOI:10.1119/5.0182191
  • Accession Number:176806119
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