{"id":3357,"date":"2014-04-22T23:57:37","date_gmt":"2014-04-23T03:57:37","guid":{"rendered":"http:\/\/pages.vassar.edu\/magnes\/?p=3357"},"modified":"2014-05-07T11:39:36","modified_gmt":"2014-05-07T15:39:36","slug":"preliminary-results-electric-fields-of-spherical-objects","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2014\/04\/22\/preliminary-results-electric-fields-of-spherical-objects\/","title":{"rendered":"Preliminary Results – Electric Fields of Spherical Objects"},"content":{"rendered":"

My project is going interestingly. Using the equation of a point charge mentioned in my Project Plan, I achieved the following:<\/p>\n

\"pointchargefield\"<\/a><\/p>\n

 <\/p>\n

I was also able to successfully plot a sphere of radius 5 centered at the origin, using the SphericalPlot3D function in Mathematica 9. Superimposing the two, I achieved the following:<\/p>\n

\"sphere1field\"<\/a><\/p>\n

 <\/p>\n

Clearly, however, this is incorrect, as the field lines should begin at radius of 5 (this is a hollow sphere, with all charge q <\/em>[equal to the charge of an electron] at the surface), according to Gauss’s Law. I am having trouble getting this to work correctly. I have been experimenting doing it in one octant to get a better idea of how the functions work, but I am still stuck.<\/p>\n

\"octant1\"<\/a><\/p>\n

 <\/p>\n

My trajectory for the next week is to gain a better understanding of vector functions in general and VectorFunction3D in Mathematica so that I can make better progress. My Mathematica file can be found here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

My project is going interestingly. Using the equation of a point charge mentioned in my Project Plan, I achieved the following:   I was also able to successfully plot a sphere of radius 5 centered at the origin, using the SphericalPlot3D function in Mathematica 9. Superimposing the two, I achieved the following:   Clearly, however, […]<\/p>\n","protected":false},"author":2606,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4101,54193,54190],"tags":[],"class_list":["post-3357","post","type-post","status-publish","format-standard","hentry","category-advanced-em","category-ramy","category-spring-2014"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3357","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\/2606"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=3357"}],"version-history":[{"count":3,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3357\/revisions"}],"predecessor-version":[{"id":3370,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3357\/revisions\/3370"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=3357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=3357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=3357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}