{"id":3049,"date":"2014-04-22T18:32:04","date_gmt":"2014-04-22T22:32:04","guid":{"rendered":"http:\/\/pages.vassar.edu\/magnes\/?p=3049"},"modified":"2014-04-22T18:32:04","modified_gmt":"2014-04-22T22:32:04","slug":"preliminary-data-2","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2014\/04\/22\/preliminary-data-2\/","title":{"rendered":"Preliminary Data"},"content":{"rendered":"<p>Using Gauss&#8217;s Law for the Electric Field, I found the electric field for a conducting cylinder with a charge density<\/p>\n<p><a href=\"http:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/CodeCogsEqn.gif\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3059\" alt=\"CodeCogsEqn\" src=\"http:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/CodeCogsEqn.gif\" width=\"51\" height=\"17\" \/><\/a>\u00a0. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Eq.1)<\/p>\n<p>The end result is the equation<\/p>\n<p><img decoding=\"async\" id=\"equationview\" title=\"This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.\" alt=\"\" src=\"http:\/\/latex.codecogs.com\/gif.latex?%5Coverrightarrow%7BE%7D%3D%5Cfrac%7Bks%5E%7B2%7D%7D%7B3%5Cepsilon%20_%7B0%7D%7D%20%5Cwidehat%7Bs%7D\" \/>. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Eq.2)<\/p>\n<p>With this, I was able to model the following.<\/p>\n<p><a href=\"http:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/Efield-for-conductors.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-3062\" alt=\"Efield for conductors\" src=\"http:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/Efield-for-conductors-300x295.png\" width=\"300\" height=\"295\" srcset=\"https:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/Efield-for-conductors-300x295.png 300w, https:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/Efield-for-conductors.png 368w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(Figure 1)<\/p>\n<p>Here is a photo of what is occurring on the inside of the cylinder. As you can see in Figure 2, the Gaussian surface would be placed in the center of the cylinder where the vector fields start and are directed radially outward. \u00a0As implied by Equation 2, the electric field is directly proportional to the radius of the cylinder.<\/p>\n<p><a href=\"http:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/efield-inside.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-3187\" alt=\"efield inside\" src=\"http:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/efield-inside-300x297.png\" width=\"300\" height=\"297\" srcset=\"https:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/efield-inside-300x297.png 300w, https:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/efield-inside-150x150.png 150w, https:\/\/pages.vassar.edu\/magnes\/files\/2014\/04\/efield-inside.png 408w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Figure 2)<\/p>\n<p>I am currently working on modeling the magnetic field.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Using Gauss&#8217;s Law for the Electric Field, I found the electric field for a conducting cylinder with a charge density \u00a0. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (Eq.1) The end [&hellip;]<\/p>\n","protected":false},"author":2424,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[188,54195],"tags":[],"class_list":["post-3049","post","type-post","status-publish","format-standard","hentry","category-mathematica","category-tewa"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3049","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/users\/2424"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=3049"}],"version-history":[{"count":16,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3049\/revisions"}],"predecessor-version":[{"id":3223,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3049\/revisions\/3223"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=3049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=3049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=3049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}