A note on Purcell's basic explanation of magnetic forces
In the 1960s, E.M. Purcell presented a basic explanation of the magnetic force experienced by a test charge moving parallel to a stationary current-carrying wire. According to Purcell's derivation, this force results from the difference between the relativistic length contraction of the distanc...
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description | In the 1960s, E.M. Purcell presented a basic explanation of the magnetic force experienced by a test charge moving parallel to a stationary current-carrying wire. According to Purcell's derivation, this force results from the difference between the relativistic length contraction of the distance among the stationary positive charges of the wire and the relativistic length contraction of the distance among the negative charges moving in the wire when the charges are observed in the rest frame of the test charge. The contraction difference generates a charge density imbalance that, in the rest frame of the test charge, is experienced as an electrostatic force, while, in the lab frame, is perceived as the magnetic force. In the present paper, we show that Purcell's approach is problematic since it generates inconsistencies and paradoxes. We maintain that Purcell's derivation has only an illustrative and expository value and should not be taken literally as describing something that really and physically happens in the wire. Furthermore, we believe that the difficulties pointed out here should be explicitly presented and discussed when introducing Purcell's approach in physics courses at the undergraduate and graduate levels. |
doi_str_mv | 10.48550/arxiv.2108.07169 |
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Purcell presented a basic explanation of the magnetic force experienced by a test charge moving parallel to a stationary current-carrying wire. According to Purcell's derivation, this force results from the difference between the relativistic length contraction of the distance among the stationary positive charges of the wire and the relativistic length contraction of the distance among the negative charges moving in the wire when the charges are observed in the rest frame of the test charge. The contraction difference generates a charge density imbalance that, in the rest frame of the test charge, is experienced as an electrostatic force, while, in the lab frame, is perceived as the magnetic force. In the present paper, we show that Purcell's approach is problematic since it generates inconsistencies and paradoxes. We maintain that Purcell's derivation has only an illustrative and expository value and should not be taken literally as describing something that really and physically happens in the wire. Furthermore, we believe that the difficulties pointed out here should be explicitly presented and discussed when introducing Purcell's approach in physics courses at the undergraduate and graduate levels.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.2108.07169</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Charge density ; Derivation ; Magnetic fields ; Physics - General Physics ; Relativistic effects ; Wire</subject><ispartof>arXiv.org, 2023-11</ispartof><rights>2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). 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We maintain that Purcell's derivation has only an illustrative and expository value and should not be taken literally as describing something that really and physically happens in the wire. Furthermore, we believe that the difficulties pointed out here should be explicitly presented and discussed when introducing Purcell's approach in physics courses at the undergraduate and graduate levels.</description><subject>Charge density</subject><subject>Derivation</subject><subject>Magnetic fields</subject><subject>Physics - General Physics</subject><subject>Relativistic effects</subject><subject>Wire</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj8tqwzAQRUWh0JDmA7qqoIuu7Mojy5aWIfQFgXaRvRnJUnFwLFeyS_r3VZKu5nWZew8hdwXLSykEe8Jw7H5yKJjMWV1U6oosgPMikyXADVnFuGeMQVWDEHxB5JoOfrLUD_RzDsb2_WOkGmNnqD2OPQ44denmHT3g12CntHc-6eItuXbYR7v6r0uye3nebd6y7cfr-2a9zVBAmRngunamVsCUTAl0lWy10lJKNIphrdtWmlYZl1rbtmV1GpEzLJwS4PiS3F_enrGaMXQHDL_NCa854yXFw0UxBv892zg1ez-HIWVqQFTJF5go-R-uFlIs</recordid><startdate>20231111</startdate><enddate>20231111</enddate><creator>D'Abramo, Germano</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>GOX</scope></search><sort><creationdate>20231111</creationdate><title>A note on Purcell's basic explanation of magnetic forces</title><author>D'Abramo, Germano</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a524-c23b7fc792098842b6255b9b888ac90a7bdd8cd9cfa7bedd46d8cda30a1f952f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Charge density</topic><topic>Derivation</topic><topic>Magnetic fields</topic><topic>Physics - General Physics</topic><topic>Relativistic effects</topic><topic>Wire</topic><toplevel>online_resources</toplevel><creatorcontrib>D'Abramo, Germano</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>D'Abramo, Germano</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on Purcell's basic explanation of magnetic forces</atitle><jtitle>arXiv.org</jtitle><date>2023-11-11</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>In the 1960s, E.M. Purcell presented a basic explanation of the magnetic force experienced by a test charge moving parallel to a stationary current-carrying wire. According to Purcell's derivation, this force results from the difference between the relativistic length contraction of the distance among the stationary positive charges of the wire and the relativistic length contraction of the distance among the negative charges moving in the wire when the charges are observed in the rest frame of the test charge. The contraction difference generates a charge density imbalance that, in the rest frame of the test charge, is experienced as an electrostatic force, while, in the lab frame, is perceived as the magnetic force. In the present paper, we show that Purcell's approach is problematic since it generates inconsistencies and paradoxes. We maintain that Purcell's derivation has only an illustrative and expository value and should not be taken literally as describing something that really and physically happens in the wire. Furthermore, we believe that the difficulties pointed out here should be explicitly presented and discussed when introducing Purcell's approach in physics courses at the undergraduate and graduate levels.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.2108.07169</doi><oa>free_for_read</oa></addata></record> |
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subjects | Charge density Derivation Magnetic fields Physics - General Physics Relativistic effects Wire |
title | A note on Purcell's basic explanation of magnetic forces |
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