{"id":145530,"date":"2024-09-27T11:21:06","date_gmt":"2024-09-27T11:21:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=145530"},"modified":"2024-09-27T11:21:09","modified_gmt":"2024-09-27T11:21:09","slug":"a-2-0-m-long-conducting-wire-is-formed-into-a-square-and-placed-in-the-horizontal-x-y-plane","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/27\/a-2-0-m-long-conducting-wire-is-formed-into-a-square-and-placed-in-the-horizontal-x-y-plane\/","title":{"rendered":"A 2.0-m long conducting wire is formed into a square and placed in the horizontal x-y plane"},"content":{"rendered":"\n<p>A 2.0-m long conducting wire is formed into a square and placed in the horizontal x-y plane. A uniform magnetic field is oriented 30.0\u00b0 above the horizontal with a strength of 9.0 T. What is the magnetic flux through the square?<\/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 calculate the magnetic flux (( \\Phi_B )) through the square loop formed by the conducting wire, we can use the formula:<\/p>\n\n\n\n<p>[<br>\\Phi_B = B \\cdot A \\cdot \\cos(\\theta)<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( B ) is the magnetic field strength (in teslas),<\/li>\n\n\n\n<li>( A ) is the area of the square (in square meters),<\/li>\n\n\n\n<li>( \\theta ) is the angle between the magnetic field and the normal to the surface of the square.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Determine the Area of the Square<\/h3>\n\n\n\n<p>Given that the wire is 2.0 m long and is formed into a square, each side length (( L )) of the square can be calculated as follows:<\/p>\n\n\n\n<p>[<br>L = \\frac{2.0 \\, \\text{m}}{4} = 0.5 \\, \\text{m}<br>]<\/p>\n\n\n\n<p>The area (( A )) of the square is:<\/p>\n\n\n\n<p>[<br>A = L^2 = (0.5 \\, \\text{m})^2 = 0.25 \\, \\text{m}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Identify the Magnetic Field Strength and Angle<\/h3>\n\n\n\n<p>The strength of the magnetic field (( B )) is given as 9.0 T. The magnetic field is oriented at 30.0\u00b0 above the horizontal. The angle ( \\theta ) we need is the angle between the magnetic field and the normal to the surface of the square. Since the square is in the horizontal x-y plane, the normal to this surface points vertically (90\u00b0). Therefore, the angle ( \\theta ) is:<\/p>\n\n\n\n<p>[<br>\\theta = 90\u00b0 &#8211; 30\u00b0 = 60\u00b0<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the Magnetic Flux<\/h3>\n\n\n\n<p>Now we can plug these values into the magnetic flux formula:<\/p>\n\n\n\n<p>[<br>\\Phi_B = B \\cdot A \\cdot \\cos(\\theta)<br>]<\/p>\n\n\n\n<p>Substituting the values:<\/p>\n\n\n\n<p>[<br>\\Phi_B = 9.0 \\, \\text{T} \\cdot 0.25 \\, \\text{m}^2 \\cdot \\cos(60\u00b0)<br>]<\/p>\n\n\n\n<p>Since ( \\cos(60\u00b0) = 0.5 ):<\/p>\n\n\n\n<p>[<br>\\Phi_B = 9.0 \\, \\text{T} \\cdot 0.25 \\, \\text{m}^2 \\cdot 0.5<br>]<br>[<br>\\Phi_B = 9.0 \\cdot 0.125 = 1.125 \\, \\text{Wb} \\quad (\\text{Weber})<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The magnetic flux through the square is ( \\Phi_B = 1.125 \\, \\text{Wb} ). This calculation illustrates how the orientation of the magnetic field relative to the area affects the magnetic flux. A smaller angle (closer to 0\u00b0) increases the flux, while larger angles reduce it. The maximum flux occurs when the field is perpendicular to the area, which is when ( \\theta = 0\u00b0).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A 2.0-m long conducting wire is formed into a square and placed in the horizontal x-y plane. A uniform magnetic field is oriented 30.0\u00b0 above the horizontal with a strength of 9.0 T. What is the magnetic flux through the square? The Correct Answer and Explanation is : To calculate the magnetic flux (( \\Phi_B [&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-145530","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145530","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=145530"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145530\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145530"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}