{"id":"https://openalex.org/W4404591015","doi":"https://doi.org/10.1119/5.0176852","title":"Teaching magnetism with bivectors","display_name":"Teaching magnetism with bivectors","publication_year":2024,"publication_date":"2024-11-21","ids":{"openalex":"https://openalex.org/W4404591015","doi":"https://doi.org/10.1119/5.0176852"},"language":"en","primary_location":{"id":"doi:10.1119/5.0176852","doi":"https://doi.org/10.1119/5.0176852","is_oa":false,"landing_page_url":"https://doi.org/10.1119/5.0176852","pdf_url":null,"source":{"id":"https://openalex.org/S38866342","display_name":"American Journal of Physics","issn_l":"0002-9505","issn":["0002-9505","1943-2909"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2309.02548","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070869863","display_name":"Steuard Jensen","orcid":"https://orcid.org/0000-0002-5434-0460","observed_orcids":["https://orcid.org/0000-0002-5434-0460"]},"institutions":[{"id":"https://openalex.org/I186589156","display_name":"Alma College","ror":"https://ror.org/02pdzen98","country_code":"US","type":"education","lineage":["https://openalex.org/I186589156"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Steuard Jensen","raw_affiliation_strings":["Department of Physics and Engineering, Alma College , Alma, Michigan 48801"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Engineering, Alma College , Alma, Michigan 48801","institution_ids":["https://openalex.org/I186589156"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070869863"],"corresponding_institution_ids":["https://openalex.org/I186589156"],"apc_list":null,"apc_paid":null,"fwci":0.1593,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.36456011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"92","issue":"12","first_page":"936","last_page":"944"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11683","display_name":"Quantum and Classical Electrodynamics","score":0.6884999871253967,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11683","display_name":"Quantum and Classical Electrodynamics","score":0.6884999871253967,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10072","display_name":"Science Education and Pedagogy","score":0.10329999774694443,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.046799998730421066,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bivectors","display_name":"bivectors","score":0.8820000290870667},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"magnetic field","score":0.9200000166893005},{"id":"https://openalex.org/keywords/cross-product","display_name":"cross product","score":0.6100000143051147},{"id":"https://openalex.org/keywords/antisymmetric-matrices","display_name":"antisymmetric matrices","score":0.6320000290870667},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.9139999747276306},{"id":"https://openalex.org/keywords/physics-education","display_name":"physics education","score":0.675000011920929},{"id":"https://openalex.org/keywords/student-misconceptions","display_name":"student misconceptions","score":0.5440000295639038},{"id":"https://openalex.org/keywords/theory-of-relativity","display_name":"relativity","score":0.6119999885559082},{"id":"https://openalex.org/keywords/extra-dimensions","display_name":"extra dimensions","score":0.8420000076293945}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7884349822998047},{"id":"https://openalex.org/C197162081","wikidata":"https://www.wikidata.org/wiki/Q3294789","display_name":"Magnetism","level":2,"score":0.7195630073547363},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3921665549278259},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.35709863901138306},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21418362855911255}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1119/5.0176852","doi":"https://doi.org/10.1119/5.0176852","is_oa":false,"landing_page_url":"https://doi.org/10.1119/5.0176852","pdf_url":null,"source":{"id":"https://openalex.org/S38866342","display_name":"American Journal of Physics","issn_l":"0002-9505","issn":["0002-9505","1943-2909"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Physics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2309.02548","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.02548","pdf_url":"https://arxiv.org/pdf/2309.02548","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2309.02548","doi":"https://doi.org/10.48550/arxiv.2309.02548","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.02548","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2309.02548","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.02548","pdf_url":"https://arxiv.org/pdf/2309.02548","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality education","score":0.6164000034332275}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404591015.pdf","grobid_xml":"https://content.openalex.org/works/W4404591015.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1598979961","https://openalex.org/W1985807403","https://openalex.org/W1987069567","https://openalex.org/W1987750830","https://openalex.org/W2047910962","https://openalex.org/W2052387963","https://openalex.org/W2061855547","https://openalex.org/W2063719974","https://openalex.org/W2071140701","https://openalex.org/W2072306379","https://openalex.org/W2074321591","https://openalex.org/W2141673608","https://openalex.org/W2170062821","https://openalex.org/W2322114488","https://openalex.org/W2962807533","https://openalex.org/W2962913678","https://openalex.org/W3089089806","https://openalex.org/W4388885874"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W2271181815"],"abstract_inverted_index":{"The":[0],"magnetic":[1,45],"field":[2],"is":[3],"traditionally":[4],"presented":[5],"as":[6,54],"a":[7],"(pseudo)vector":[8],"quantity,":[9],"tied":[10],"closely":[11],"to":[12,18,85,101,110],"the":[13],"cross":[14,88],"product.":[15],"Though":[16],"familiar":[17,111],"experts,":[19],"many":[20],"students":[21],"find":[22],"these":[23],"ideas":[24],"challenging":[25],"and":[26,106],"full":[27],"of":[28],"subtleties.":[29],"Building":[30],"on":[31],"earlier":[32],"work":[33],"in":[34,69,92],"rotational":[35],"physics,":[36],"we":[37],"present":[38],"an":[39,60],"alternative":[40],"pedagogical":[41],"approach":[42],"that":[43],"describes":[44],"fields":[46],"using":[47],"bivectors.":[48],"These":[49],"objects":[50],"can":[51],"be":[52],"visualized":[53],"oriented":[55],"tiles":[56],"whose":[57],"components":[58],"form":[59],"antisymmetric":[61],"matrix.":[62],"Historically,":[63],"bivectors":[64],"have":[65],"been":[66],"mostly":[67],"used":[68],"specialized":[70],"contexts":[71],"like":[72],"spacetime":[73],"classification":[74],"or":[75],"geometric":[76],"algebra,":[77],"but":[78],"they":[79],"are":[80],"not":[81],"necessarily":[82],"more":[83],"complicated":[84],"understand":[86],"than":[87],"products.":[89],"Teaching":[90],"magnetism":[91],"this":[93],"language":[94],"addresses":[95],"common":[96],"student":[97],"difficulties,":[98],"generalizes":[99],"directly":[100],"relativity":[102],"(and":[103],"extra":[104],"dimensions),":[105],"brings":[107],"fresh":[108],"insight":[109],"ideas.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
