Derivation of the Field Due to a Magnetic Dipole without Use of the Vector Potential

Autor/inn/en	Proctor, John E.; Gould, Harvey Thomas
Titel	Derivation of the Field Due to a Magnetic Dipole without Use of the Vector Potential
Quelle	In: Physics Teacher, 61 (2023) 1, S.40-42 (3 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Proctor, John E.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0031-921X
Schlagwörter	Science Instruction; Energy; Magnets; College Science; Undergraduate Study; Scientific Concepts; Concept Formation; Mathematics + Suchen Sie Ihr Suchwort? Teaching of science; Science education; Natural sciences Lessons; Naturwissenschaftlicher Unterricht; Energie; Stabmagnet; Grundstudium; Concept learning; Begriffsbildung; Mathematik
Abstract	The mathematical form of the magnetic field due to a current loop, and the fact that it is identical to the electric field due to an electric dipole in the far field, are fundamental to our understanding of electromagnetism. While undergraduate level electromagnetism textbooks usually derive the electric field from an electric dipole, few derive the magnetic field from a current loop. Most simply state it without proof, or perform the derivation for simpler cases such as the on-axis field. Those that perform the derivation use the magnetic vector potential, a relatively advanced concept that most undergraduate students would not encounter until their final year of study, if at all. Here, a simple derivation to obtain the magnetic field due to a current loop in the far-field approximation is presented. The derivation begins from the Biot-Savart law and does not require the vector potential. The problem is set up so that only a single integration is necessary (from angle [alpha] = 0 to [alpha] = 2[pi] around the current loop), and the result is compared with that for the electric field surrounding an electric dipole. (As Provided).
Anmerkungen	American Association of Physics Teachers. One Physics Ellipse, College Park, MD 20740. Tel: 301-209-3300; Fax: 301-209-0845; e-mail: pubs@aapt.org; Web site: http://aapt.scitation.org/journal/pte
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01