When the charge on a planar conductor is a function of its curvature
While there is no general relationship between the electric charge density on a conducting surface and its curvature, the two quantities can be functionally related in special circumstances. This paper presents a complete classification of two-dimensional conductors for which charge density is a fun...
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| Veröffentlicht in: | Journal of mathematical physics 2014-12, Vol.55 (12), p.1 |
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| container_title | Journal of mathematical physics |
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| creator | Cross, Daniel J |
| description | While there is no general relationship between the electric charge density on a conducting surface and its curvature, the two quantities can be functionally related in special circumstances. This paper presents a complete classification of two-dimensional conductors for which charge density is a function of boundary curvature. Whenever the curvature function is non-injective, the conductor must transform under one of the planar symmetry groups. In particular, for the charge density on a closed conductor with smooth boundary to be a function of its curvature, the conductor must possess dihedral symmetry with a mirror line running through each curvature extremum. Several examples are presented along with explicit charge-curvature functions. Both increasing and decreasing functions were found. |
| doi_str_mv | 10.1063/1.4903168 |
| format | Article |
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This paper presents a complete classification of two-dimensional conductors for which charge density is a function of boundary curvature. Whenever the curvature function is non-injective, the conductor must transform under one of the planar symmetry groups. In particular, for the charge density on a closed conductor with smooth boundary to be a function of its curvature, the conductor must possess dihedral symmetry with a mirror line running through each curvature extremum. Several examples are presented along with explicit charge-curvature functions. 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Both increasing and decreasing functions were found.</description><subject>Boundary conditions</subject><subject>Charge density</subject><subject>Conduction</subject><subject>Conductors</subject><subject>Curvature</subject><subject>Density</subject><subject>Electric currents</subject><subject>Physics</subject><subject>Smooth boundaries</subject><subject>Symmetry</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEYhIMoWFcP_oOAJw9b33xu9ij1EwpeFI8hm76xW-qmJlnBf-9Ke_YyA8PDDAwhlwzmDLS4YXPZgmDaHJEZA9PWjVbmmMwAOK-5NOaUnOW8AWDMSDkjd-9rHGhZI_Vrlz6QxoE6utu6wSXq47AafYmJ9nlKwzj40k9ADLQvmfoxfbsyJjwnJ8FtM14cvCJvD_evi6d6-fL4vLhd1p4bVWqlAKRoOGJYAYNVh53GBjxXjQHegfQdIEMjgAfdsFY4Dd44FI3GoIwRFbna9-5S_BoxF7uJYxqmScsZ17IVQrX_UUzLRrSGT1qR6z3lU8w5YbC71H-69GMZ2L8rLbOHK8Uv8b1i4g</recordid><startdate>20141201</startdate><enddate>20141201</enddate><creator>Cross, Daniel J</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope></search><sort><creationdate>20141201</creationdate><title>When the charge on a planar conductor is a function of its curvature</title><author>Cross, Daniel J</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c285t-55004372eefd010dbeb6e70c257802b04cb0e1e8302f67193a60c8ae376ef5883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Boundary conditions</topic><topic>Charge density</topic><topic>Conduction</topic><topic>Conductors</topic><topic>Curvature</topic><topic>Density</topic><topic>Electric currents</topic><topic>Physics</topic><topic>Smooth boundaries</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cross, Daniel J</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cross, Daniel J</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>When the charge on a planar conductor is a function of its curvature</atitle><jtitle>Journal of mathematical physics</jtitle><date>2014-12-01</date><risdate>2014</risdate><volume>55</volume><issue>12</issue><spage>1</spage><pages>1-</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><abstract>While there is no general relationship between the electric charge density on a conducting surface and its curvature, the two quantities can be functionally related in special circumstances. This paper presents a complete classification of two-dimensional conductors for which charge density is a function of boundary curvature. Whenever the curvature function is non-injective, the conductor must transform under one of the planar symmetry groups. In particular, for the charge density on a closed conductor with smooth boundary to be a function of its curvature, the conductor must possess dihedral symmetry with a mirror line running through each curvature extremum. Several examples are presented along with explicit charge-curvature functions. Both increasing and decreasing functions were found.</abstract><cop>New York</cop><pub>American Institute of Physics</pub><doi>10.1063/1.4903168</doi></addata></record> |
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| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2014-12, Vol.55 (12), p.1 |
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| language | eng |
| recordid | cdi_proquest_journals_2126493359 |
| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Boundary conditions Charge density Conduction Conductors Curvature Density Electric currents Physics Smooth boundaries Symmetry |
| title | When the charge on a planar conductor is a function of its curvature |
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