{"id":144418,"date":"2015-11-12T03:00:00","date_gmt":"2015-11-12T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=57d6da54ec4d26c7fd7df11dd6c29488"},"modified":"2015-11-12T03:00:00","modified_gmt":"2015-11-12T00:00:00","slug":"the-helmholtz-decomposition-revisited","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=144418","title":{"rendered":"The Helmholtz decomposition revisited"},"content":{"rendered":"<p>In electrodynamics it is generally accepted that only vector fields decaying asymptotically more<br \/>\nstrongly than the inverse of the distance can be split into an irrotational and a solenoidal part,<br \/>\nalthough this decomposition can clearly\u00a0be applied to all vector fields that vanish asymptotically<br \/>\nwith a small power. Moreover this decomposition is valid even for vector fields that diverge weaker<br \/>\nthan linearly. A simple proof is presented.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In electrodynamics it is generally accepted that only vector fields decaying asymptotically more<br \/>\nstrongly than the inverse of the distance can be split into an irrotational and a solenoidal part,<br \/>\nalthough this decomposition can clearly\u00a0be applied to&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-144418","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/144418","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=144418"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/144418\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=144418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=144418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=144418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}