On the electric field at the surface of a uniformly-charged cylindrical shell
In some recent papers, I have shown that the electric field at the surface of a uniformly-charged spherical shell (or a conducting sphere, since the charge distribution is the same) evaluates to half the field discontinuity across its surface. For a cylindrical shell, however, only a simple applicat...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Portuguese |
| Published: |
Sociedade Brasileira de Física
2025-01-01
|
| Series: | Revista Brasileira de Ensino de Física |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172025000100901&lng=en&tlng=en |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832592549606326272 |
|---|---|
| author | Fábio M.S. Lima |
| author_facet | Fábio M.S. Lima |
| author_sort | Fábio M.S. Lima |
| collection | DOAJ |
| description | In some recent papers, I have shown that the electric field at the surface of a uniformly-charged spherical shell (or a conducting sphere, since the charge distribution is the same) evaluates to half the field discontinuity across its surface. For a cylindrical shell, however, only a simple application of Gauss’s law for infinitely long shells is found in textbooks, which yields a field that is null inside the shell and, outside it, decays with the inverse of the distance to the central axis. Nothing is said for points located exactly at the shell. For those points, the amount of charge surrounded by a Gaussian surface coinciding with the shell is undefined, which makes the application of Gauss’s law inconclusive. In this note, by treating a cylindrical shell as a collection of identical charged rings, I derive that electric field in terms of elliptic integrals and then I show that, for very long shells, it reduces to half the field discontinuity across the shell. |
| format | Article |
| id | doaj-art-1154102870554b84999c7fbcf1ad8923 |
| institution | Kabale University |
| issn | 1806-9126 |
| language | Portuguese |
| publishDate | 2025-01-01 |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj-art-1154102870554b84999c7fbcf1ad89232025-01-21T07:35:48ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-91262025-01-014710.1590/1806-9126-rbef-2024-0312On the electric field at the surface of a uniformly-charged cylindrical shellFábio M.S. Limahttps://orcid.org/0000-0001-5884-6621In some recent papers, I have shown that the electric field at the surface of a uniformly-charged spherical shell (or a conducting sphere, since the charge distribution is the same) evaluates to half the field discontinuity across its surface. For a cylindrical shell, however, only a simple application of Gauss’s law for infinitely long shells is found in textbooks, which yields a field that is null inside the shell and, outside it, decays with the inverse of the distance to the central axis. Nothing is said for points located exactly at the shell. For those points, the amount of charge surrounded by a Gaussian surface coinciding with the shell is undefined, which makes the application of Gauss’s law inconclusive. In this note, by treating a cylindrical shell as a collection of identical charged rings, I derive that electric field in terms of elliptic integrals and then I show that, for very long shells, it reduces to half the field discontinuity across the shell.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172025000100901&lng=en&tlng=enElectric fieldsGauss’s lawCylindrical shell |
| spellingShingle | Fábio M.S. Lima On the electric field at the surface of a uniformly-charged cylindrical shell Revista Brasileira de Ensino de Física Electric fields Gauss’s law Cylindrical shell |
| title | On the electric field at the surface of a uniformly-charged cylindrical shell |
| title_full | On the electric field at the surface of a uniformly-charged cylindrical shell |
| title_fullStr | On the electric field at the surface of a uniformly-charged cylindrical shell |
| title_full_unstemmed | On the electric field at the surface of a uniformly-charged cylindrical shell |
| title_short | On the electric field at the surface of a uniformly-charged cylindrical shell |
| title_sort | on the electric field at the surface of a uniformly charged cylindrical shell |
| topic | Electric fields Gauss’s law Cylindrical shell |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172025000100901&lng=en&tlng=en |
| work_keys_str_mv | AT fabiomslima ontheelectricfieldatthesurfaceofauniformlychargedcylindricalshell |