{"id":3795,"date":"2014-04-30T10:23:27","date_gmt":"2014-04-30T14:23:27","guid":{"rendered":"http:\/\/pages.vassar.edu\/magnes\/?p=3795"},"modified":"2014-05-07T11:39:09","modified_gmt":"2014-05-07T15:39:09","slug":"final-data-e-fields-of-spherical-objects","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2014\/04\/30\/final-data-e-fields-of-spherical-objects\/","title":{"rendered":"Final Data – E Fields of Spherical Objects"},"content":{"rendered":"

I began by modeling the electric field for a point charge\u00a0+q<\/em>, equal to the value of an elementary charge.<\/p>\n

\"phys1\"<\/a><\/p>\n

 <\/p>\n

I also modeled the electric field of a point charge of -q<\/em>.<\/p>\n

\"phys2\"<\/a><\/p>\n

 <\/p>\n

Next, I attempted to model the electric field due to spherical hollow conductor with total charge\u00a0+q.<\/em>\u00a0<\/em>First, I graphed a sphere of radius 5 using Mathematica’s SphericalPlot3D function. I superimposed the electric field of a positive point charge over this sphere, knowing that this would be incorrect. By Gauss’s Law, the stated configuration would result in an electric field of 0 inside of the spherical conductor, and an electric field following\u00a0$\\textbf{E} = \\frac{1}{4 \\pi \\epsilon_0} \\frac{q}{r^2} \\mathbf{\\hat{r}} $ for r > 5. The following image shows a partially transparent sphere with an electric field inside of it, violating Gauss’s Law.<\/p>\n

\"phys3\"<\/a><\/p>\n

 <\/p>\n

However, thanks to Brian Deer, I learned to use Mathematica’s RegionFunction, which allowed me to specify which regions of the graph on which the vector function would apply. The following now shows a hollow conductor of radius 3, with an electric field only present outside of it. Unfortunately, this step took a lot of time to work out, as I tried many different ideas to only get the field to show for certain radius values (i.e. be 0 inside of the conductor). I was unaware of RegionFunction, and even when I did learn what it was, I had trouble getting it to work with my model.<\/p>\n

\"phys4\"<\/a><\/p>\n

 <\/p>\n

My updated Mathematica file can be found here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

I began by modeling the electric field for a point charge\u00a0+q, equal to the value of an elementary charge.   I also modeled the electric field of a point charge of -q.   Next, I attempted to model the electric field due to spherical hollow conductor with total charge\u00a0+q.\u00a0First, I graphed a sphere of radius […]<\/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-3795","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\/3795","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=3795"}],"version-history":[{"count":3,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3795\/revisions"}],"predecessor-version":[{"id":3817,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/3795\/revisions\/3817"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=3795"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=3795"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=3795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}