{"id":218363,"date":"2025-05-23T17:07:53","date_gmt":"2025-05-23T17:07:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218363"},"modified":"2025-05-23T17:07:55","modified_gmt":"2025-05-23T17:07:55","slug":"how-should-the-integral-in-gausss-law-be-evaluated","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/23\/how-should-the-integral-in-gausss-law-be-evaluated\/","title":{"rendered":"How should the integral in Gauss’s law be evaluated"},"content":{"rendered":"\n

How should the integral in Gauss’s law be evaluated?<\/p>\n\n\n\n

around the perimeter of a closed loop<\/p>\n\n\n\n

over the surface bounded by a closed loop<\/p>\n\n\n\n

over a closed surface<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong>
Over a closed surface<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

Gauss\u2019s Law is one of Maxwell\u2019s equations and is a fundamental law in electromagnetism. It relates the electric flux through a closed surface to the electric charge enclosed by that surface. Mathematically, it is expressed as: \u222eclosed surfaceE\u20d7\u22c5dA\u20d7=Qinside\u03b50\\oint_{\\text{closed surface}} \\vec{E} \\cdot d\\vec{A} = \\frac{Q_{\\text{inside}}}{\\varepsilon_0}<\/p>\n\n\n\n

Here,<\/p>\n\n\n\n

    \n
  • E\u20d7\\vec{E} is the electric field vector,<\/li>\n\n\n\n
  • dA\u20d7d\\vec{A} is the differential area vector on the closed surface (pointing outward),<\/li>\n\n\n\n
  • QinsideQ_{\\text{inside}} is the total electric charge enclosed within the surface, and<\/li>\n\n\n\n
  • \u03b50\\varepsilon_0 is the vacuum permittivity constant.<\/li>\n\n\n\n
  • <\/li>\n<\/ul>\n\n\n\n

    The integral symbol with a circle (\u222e) indicates a surface integral over a closed surface<\/strong>. This distinguishes Gauss\u2019s Law from other types of integrals such as line integrals (around a loop) or surface integrals over open surfaces.<\/p>\n\n\n\n

    A closed surface<\/strong> is any surface that completely encloses a volume\u2014like the surface of a sphere, cube, or cylinder with end caps. The key is that there is no boundary; the surface forms a complete shell.<\/p>\n\n\n\n

    This law is especially powerful when applied to systems with high symmetry (spherical, cylindrical, or planar), where it can simplify the calculation of electric fields. For example, using a spherical Gaussian surface around a point charge allows easy computation of the radial electric field using symmetry and the inverse-square law.<\/p>\n\n\n\n

    If the integral were taken “around the perimeter of a closed loop,” it would represent a line integral, not a surface integral, and would apply to Faraday\u2019s Law of Induction\u2014not Gauss\u2019s Law. Similarly, \u201cover the surface bounded by a closed loop\u201d refers to an open surface, which is not applicable to Gauss\u2019s Law.<\/p>\n\n\n\n

    Thus, Gauss\u2019s Law always involves integrating over a closed surface<\/strong>.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    How should the integral in Gauss’s law be evaluated? around the perimeter of a closed loop over the surface bounded by a closed loop over a closed surface The Correct Answer and Explanation is: Correct Answer:Over a closed surface Explanation: Gauss\u2019s Law is one of Maxwell\u2019s equations and is a fundamental law in electromagnetism. It […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-218363","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=218363"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218363\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}