{"id":1635,"date":"2012-04-18T01:24:34","date_gmt":"2012-04-18T05:24:34","guid":{"rendered":"http:\/\/blogs.vassar.edu\/magnes\/?p=1635"},"modified":"2013-07-11T10:28:29","modified_gmt":"2013-07-11T14:28:29","slug":"intro-to-preliminary-results","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2012\/04\/18\/intro-to-preliminary-results\/","title":{"rendered":"Intro To Preliminary Results"},"content":{"rendered":"

As it turns out, the equations for magnetic fields and forces that I was hoping to plot in Mathematica are too complicated for Mathematica to handle. I am unsure whether this drawback just applies to my Student version of Mathematica, or if my personal computer is to blame. However, I took a slight deviation to begin my studies with a simpler equation to model, the equation for the magnetic force between two plates of some finite area, given by:<\/p>\n

(1) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

where \"B\" is the magnetic flux density (magnetic field strength) at a given distance above the bottom magnet, \"A\" is the common area between the two plates, and \"\mu_{0}\" is the permeability of free space. In order to easily visualize this effect, I generalized the magnetic flux density by replacing it with a constant multiple times the inverse of distance cubed (which is the relationship between magnetic field strength and distance), producing the following graph in Mathematica:<\/p>\n

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

Clearly, the force falls off extremely quickly with respect to distance, so I am expecting my other graphs to have a range of many fractions of a meter. This outcome is exactly as I would expect (ignoring any fringing effects near the edges), since the magnetic force between the two magnets decreases rapidly with distance; in my future calculations, I will expect the force on the top magnet to increase as the two get closer together, and decrease as the magnets separate, hopefully leading to a steady distance between the two over time. As soon as I can get Mathematica to accept my more complicated equations and graphs, I will post them.<\/p>\n","protected":false},"excerpt":{"rendered":"

As it turns out, the equations for magnetic fields and forces that I was hoping to plot in Mathematica are too complicated for Mathematica to handle. I am unsure whether this drawback just applies to my Student version of Mathematica, or if my personal computer is to blame. However, I took a slight deviation to […]<\/p>\n","protected":false},"author":582,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4101,26720,29905],"tags":[],"class_list":["post-1635","post","type-post","status-publish","format-standard","hentry","category-advanced-em","category-joe","category-spring-2012"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/1635","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\/582"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=1635"}],"version-history":[{"count":7,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/1635\/revisions"}],"predecessor-version":[{"id":2388,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/1635\/revisions\/2388"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=1635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=1635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=1635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}