Closed-form expressions for the magnetic fields of rectangular and circular finite-length solenoids and current loops

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This article discusses closed-form expressions for the magnetic fields produced by rectangular- and circular-shaped finite-length solenoids and current loops. The closed-form expression for the magnetic field of a rectangular-shaped finite-length solenoid is derived using the Biot–Savart law. Closed-form expressions for the magnetic fields of solenoids and current loops can be used to avoid approximations in analytical models and may reduce computation time in computer simulations.

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Hampton, S.; Lane, R. A.; Hedlof, R. M.; Phillips, R. E. & Ordonez, Carlos A. June 15, 2020.

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This article discusses closed-form expressions for the magnetic fields produced by rectangular- and circular-shaped finite-length solenoids and current loops. The closed-form expression for the magnetic field of a rectangular-shaped finite-length solenoid is derived using the Biot–Savart law. Closed-form expressions for the magnetic fields of solenoids and current loops can be used to avoid approximations in analytical models and may reduce computation time in computer simulations.

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12 p.

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Abstract: A summary of closed-form expressions for the magnetic fields produced by rectangular- and circular-shaped finite-length solenoids and current loops is provided altogether for easy reference. Each expression provides the magnetic field in all space, except locations where a current of infinitesimal thickness is considered to exist. The closed-form expression for the magnetic field of a rectangular-shaped finite-length solenoid is derived using the Biot–Savart law. Closed-form expressions for the magnetic fields of solenoids and current loops can be used to avoid approximations in analytical models and may reduce computation time in computer simulations.

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  • AIP Advances, 10(6), American Institute of Physics, June 15, 2020, pp. 1-12

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  • Publication Title: AIP Advances
  • Volume: 10
  • Issue: 6
  • Peer Reviewed: Yes

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  • June 15, 2020

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  • July 2, 2020, 3:13 p.m.

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  • Nov. 13, 2023, 2:52 p.m.

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Hampton, S.; Lane, R. A.; Hedlof, R. M.; Phillips, R. E. & Ordonez, Carlos A. Closed-form expressions for the magnetic fields of rectangular and circular finite-length solenoids and current loops, article, June 15, 2020; (https://digital.library.unt.edu/ark:/67531/metadc1703862/: accessed May 5, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Science.

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