{"id":187454,"date":"2025-02-05T03:29:15","date_gmt":"2025-02-05T03:29:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187454"},"modified":"2025-02-05T03:29:17","modified_gmt":"2025-02-05T03:29:17","slug":"in-the-figure-a-proton-is-a-distance-d-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/05\/in-the-figure-a-proton-is-a-distance-d-2\/","title":{"rendered":"In the figure a proton is a distance d \/ 2"},"content":{"rendered":"\n<p>In the figure a proton is a distance d \/ 2 ?directly above the center of a square of side d. ?What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge d.) ?Number Units&#8221;(degrees) ?This answer has no units m kg 5 ?m \/ ?s m \/ ?s^? 2 ?N J W N \/ ?m A V N \/ ?C or V \/ ?m C \/ ?m^? 2 ?C \/ ?m^? 3 ?N \u00b7 ?m^? 2 \/ ?C Units<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the <strong>electric flux<\/strong> through the square due to a proton located a distance ( d\/2 ) above its center, we use <strong>Gauss\u2019s Law<\/strong>, which states:<\/p>\n\n\n\n<p>[<br>\\Phi_E = \\frac{q_{\\text{enc}}}{\\epsilon_0}<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\Phi_E ) is the total electric flux,<\/li>\n\n\n\n<li>( q_{\\text{enc}} ) is the charge enclosed by a Gaussian surface,<\/li>\n\n\n\n<li>( \\epsilon_0 ) is the <strong>permittivity of free space<\/strong> (( 8.85 \\times 10^{-12} ) C\u00b2\/N\u00b7m\u00b2).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Consider a Cube Enclosing the Proton<\/h3>\n\n\n\n<p>The problem hints at treating the square as one <strong>face of a cube<\/strong> with edge length ( d ). If we imagine a cube of side ( d ) enclosing the proton, the proton is located <strong>symmetrically<\/strong> above the center, implying that its <strong>entire charge ( q ) is enclosed by the cube<\/strong>.<\/p>\n\n\n\n<p>Since a cube has <strong>six faces<\/strong>, and the charge is enclosed symmetrically, the <strong>total electric flux<\/strong> through the cube is:<\/p>\n\n\n\n<p>[<br>\\Phi_{\\text{total}} = \\frac{q}{\\epsilon_0}<br>]<\/p>\n\n\n\n<p>Since the charge is <strong>uniformly distributed<\/strong> among all six faces, the flux through <strong>one face<\/strong> (our square) is:<\/p>\n\n\n\n<p>[<br>\\Phi_{\\text{square}} = \\frac{q}{6\\epsilon_0}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Substitute the Charge of a Proton<\/h3>\n\n\n\n<p>A <strong>proton<\/strong> has charge:<\/p>\n\n\n\n<p>[<br>q = 1.6 \\times 10^{-19} \\text{ C}<br>]<\/p>\n\n\n\n<p>Thus, the flux through one face is:<\/p>\n\n\n\n<p>[<br>\\Phi_{\\text{square}} = \\frac{(1.6 \\times 10^{-19} \\text{ C})}{6 (8.85 \\times 10^{-12} \\text{ C\u00b2\/N\u00b7m\u00b2})}<br>]<\/p>\n\n\n\n<p>[<br>\\Phi_{\\text{square}} \\approx 3.01 \\times 10^7 \\text{ N\u00b7m\u00b2\/C}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer:<\/h3>\n\n\n\n<p>[<br>\\Phi_{\\text{square}} \\approx 3.01 \\times 10^7 \\text{ N\u00b7m\u00b2\/C}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>We used <strong>Gauss\u2019s Law<\/strong> to relate flux to charge.<\/li>\n\n\n\n<li>We imagined a cube with the square as <strong>one of six faces<\/strong>.<\/li>\n\n\n\n<li>Since the charge is at the center of the cube, flux distributes <strong>equally<\/strong> among all faces.<\/li>\n\n\n\n<li>We divided the total flux by 6 to get the flux through <strong>one face<\/strong>.<\/li>\n\n\n\n<li>Finally, we substituted the charge of a <strong>proton<\/strong> to compute the numeric result.<\/li>\n<\/ol>\n\n\n\n<p>Thus, the <strong>electric flux through the square is ( 3.01 \\times 10^7 ) N\u00b7m\u00b2\/C.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the figure a proton is a distance d \/ 2 ?directly above the center of a square of side d. ?What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge d.) ?Number Units&#8221;(degrees) ?This answer has no units m kg [&hellip;]<\/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-187454","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187454","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=187454"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187454\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187454"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187454"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}