Identities of incomplete elliptic integrals with application in electromagnetism

Carlos A. Jiménez-Carballo; Gabriela Ortiz-León

doi:10.18687/LACCEI2024.1.1.1789

Identities of incomplete elliptic integrals with application in electromagnetism

Carlos A. Jiménez-Carballo
, Gabriela Ortiz-León

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this article, a set of incomplete elliptic integrals is given to help engineering and physics students solve problems that are common in electromagnetism. First, a brief description of the elliptic integrals of the first kind and second kind is presented, followed by a list of identities of incomplete elliptic integrals involving sine and cosine functions, and finally, these identities are used to solve three physical systems: the first is the electric potential generated by a segment of a charged ring; the second is the magnetic field generated by a segment of a ring carrying a current; and the third is the magnetic field produced by an axially magnetized permanent magnet.

Original language	English
Title of host publication	Proceedings of the 22nd LACCEI International Multi-Conference for Engineering, Education and Technology
Subtitle of host publication	Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0., LACCEI 2024
Publisher	Latin American and Caribbean Consortium of Engineering Institutions
ISBN (Electronic)	9786289520781
DOIs	https://doi.org/10.18687/LACCEI2024.1.1.1789
State	Published - 2024
Event	22nd LACCEI International Multi-Conference for Engineering, Education and Technology, LACCEI 2024 - Hybrid, San Jose, Costa Rica Duration: 17 Jul 2024 → 19 Jul 2024

Publication series

Name	Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology
ISSN (Electronic)	2414-6390

Conference

Conference	22nd LACCEI International Multi-Conference for Engineering, Education and Technology, LACCEI 2024
Country/Territory	Costa Rica
City	Hybrid, San Jose
Period	17/07/24 → 19/07/24

Keywords

Elliptic integrals
electric potential
magnetic field
permanent magnet

Access to Document

10.18687/LACCEI2024.1.1.1789

Cite this

Jiménez-Carballo, C. A., & Ortiz-León, G. (2024). Identities of incomplete elliptic integrals with application in electromagnetism. In Proceedings of the 22nd LACCEI International Multi-Conference for Engineering, Education and Technology: Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0., LACCEI 2024 (Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology). Latin American and Caribbean Consortium of Engineering Institutions. https://doi.org/10.18687/LACCEI2024.1.1.1789

Jiménez-Carballo, Carlos A. ; Ortiz-León, Gabriela. / Identities of incomplete elliptic integrals with application in electromagnetism. Proceedings of the 22nd LACCEI International Multi-Conference for Engineering, Education and Technology: Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0., LACCEI 2024. Latin American and Caribbean Consortium of Engineering Institutions, 2024. (Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology).

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abstract = "In this article, a set of incomplete elliptic integrals is given to help engineering and physics students solve problems that are common in electromagnetism. First, a brief description of the elliptic integrals of the first kind and second kind is presented, followed by a list of identities of incomplete elliptic integrals involving sine and cosine functions, and finally, these identities are used to solve three physical systems: the first is the electric potential generated by a segment of a charged ring; the second is the magnetic field generated by a segment of a ring carrying a current; and the third is the magnetic field produced by an axially magnetized permanent magnet.",

keywords = "Elliptic integrals, electric potential, magnetic field, permanent magnet",

author = "Jim{\'e}nez-Carballo, \{Carlos A.\} and Gabriela Ortiz-Le{\'o}n",

note = "Publisher Copyright: {\textcopyright} 2024 Latin American and Caribbean Consortium of Engineering Institutions. All rights reserved.; 22nd LACCEI International Multi-Conference for Engineering, Education and Technology, LACCEI 2024 ; Conference date: 17-07-2024 Through 19-07-2024",

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doi = "10.18687/LACCEI2024.1.1.1789",

language = "Ingl{\'e}s",

series = "Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology",

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Jiménez-Carballo, CA & Ortiz-León, G 2024, Identities of incomplete elliptic integrals with application in electromagnetism. in Proceedings of the 22nd LACCEI International Multi-Conference for Engineering, Education and Technology: Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0., LACCEI 2024. Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology, Latin American and Caribbean Consortium of Engineering Institutions, 22nd LACCEI International Multi-Conference for Engineering, Education and Technology, LACCEI 2024, Hybrid, San Jose, Costa Rica, 17/07/24. https://doi.org/10.18687/LACCEI2024.1.1.1789

Identities of incomplete elliptic integrals with application in electromagnetism. / Jiménez-Carballo, Carlos A.; Ortiz-León, Gabriela.
Proceedings of the 22nd LACCEI International Multi-Conference for Engineering, Education and Technology: Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0., LACCEI 2024. Latin American and Caribbean Consortium of Engineering Institutions, 2024. (Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Ortiz-León, Gabriela

PY - 2024

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N2 - In this article, a set of incomplete elliptic integrals is given to help engineering and physics students solve problems that are common in electromagnetism. First, a brief description of the elliptic integrals of the first kind and second kind is presented, followed by a list of identities of incomplete elliptic integrals involving sine and cosine functions, and finally, these identities are used to solve three physical systems: the first is the electric potential generated by a segment of a charged ring; the second is the magnetic field generated by a segment of a ring carrying a current; and the third is the magnetic field produced by an axially magnetized permanent magnet.

AB - In this article, a set of incomplete elliptic integrals is given to help engineering and physics students solve problems that are common in electromagnetism. First, a brief description of the elliptic integrals of the first kind and second kind is presented, followed by a list of identities of incomplete elliptic integrals involving sine and cosine functions, and finally, these identities are used to solve three physical systems: the first is the electric potential generated by a segment of a charged ring; the second is the magnetic field generated by a segment of a ring carrying a current; and the third is the magnetic field produced by an axially magnetized permanent magnet.

KW - Elliptic integrals

KW - electric potential

KW - magnetic field

KW - permanent magnet

UR - https://www.scopus.com/pages/publications/85203845381

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DO - 10.18687/LACCEI2024.1.1.1789

M3 - Contribución a la conferencia

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T3 - Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology

BT - Proceedings of the 22nd LACCEI International Multi-Conference for Engineering, Education and Technology

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T2 - 22nd LACCEI International Multi-Conference for Engineering, Education and Technology, LACCEI 2024

Y2 - 17 July 2024 through 19 July 2024

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Jiménez-Carballo CA, Ortiz-León G. Identities of incomplete elliptic integrals with application in electromagnetism. In Proceedings of the 22nd LACCEI International Multi-Conference for Engineering, Education and Technology: Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0., LACCEI 2024. Latin American and Caribbean Consortium of Engineering Institutions. 2024. (Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology). doi: 10.18687/LACCEI2024.1.1.1789

Identities of incomplete elliptic integrals with application in electromagnetism

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