{"id":151919,"date":"2024-10-10T15:08:01","date_gmt":"2024-10-10T15:08:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=151919"},"modified":"2024-10-10T15:08:05","modified_gmt":"2024-10-10T15:08:05","slug":"a-flat-145-turn-current-carrying-loop-is-immersed-in-a-uniform-magnetic-field","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/10\/a-flat-145-turn-current-carrying-loop-is-immersed-in-a-uniform-magnetic-field\/","title":{"rendered":"A flat 145-turn current-carrying loop is immersed in a uniform magnetic field."},"content":{"rendered":"\n<p>A flat 145-turn current-carrying loop is immersed in a uniform magnetic field. The area of the loop is 6.75 cm2 and the angle between its magnetic dipole moment and the field is 31.5\u00b0. Find the strength of the magnetic field that causes a torque of 1.33 \u00d7 10-5 N\u00b7m to act on the loop when a current of 2.11 mA flows in it.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the strength of the magnetic field ( B ) that causes a torque of ( 1.33 \\times 10^{-5} \\, \\text{N} \\cdot \\text{m} ) to act on a current-carrying loop, we can use the following formula for the torque ( \\tau ) on a current-carrying loop in a magnetic field:<\/p>\n\n\n\n<p>[<br>\\tau = \\mu \\cdot B \\cdot \\sin(\\theta)<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\tau ) is the torque,<\/li>\n\n\n\n<li>( \\mu ) is the magnetic dipole moment of the loop,<\/li>\n\n\n\n<li>( B ) is the magnetic field strength,<\/li>\n\n\n\n<li>( \\theta ) is the angle between the magnetic dipole moment and the magnetic field.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the Magnetic Dipole Moment ( \\mu )<\/h3>\n\n\n\n<p>The magnetic dipole moment ( \\mu ) of a current-carrying loop is given by:<\/p>\n\n\n\n<p>[<br>\\mu = I \\cdot A \\cdot N<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( I ) is the current (in amperes),<\/li>\n\n\n\n<li>( A ) is the area of the loop (in square meters),<\/li>\n\n\n\n<li>( N ) is the number of turns of the loop.<\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( I = 2.11 \\, \\text{mA} = 2.11 \\times 10^{-3} \\, \\text{A} ),<\/li>\n\n\n\n<li>( A = 6.75 \\, \\text{cm}^2 = 6.75 \\times 10^{-4} \\, \\text{m}^2 ),<\/li>\n\n\n\n<li>( N = 145 ) turns.<\/li>\n<\/ul>\n\n\n\n<p>Now, calculate the magnetic dipole moment:<\/p>\n\n\n\n<p>[<br>\\mu = (2.11 \\times 10^{-3}) \\cdot (6.75 \\times 10^{-4}) \\cdot 145 = 2.14 \\times 10^{-4} \\, \\text{A} \\cdot \\text{m}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve for the Magnetic Field ( B )<\/h3>\n\n\n\n<p>Using the torque formula:<\/p>\n\n\n\n<p>[<br>\\tau = \\mu \\cdot B \\cdot \\sin(\\theta)<br>]<\/p>\n\n\n\n<p>Rearranging to solve for ( B ):<\/p>\n\n\n\n<p>[<br>B = \\frac{\\tau}{\\mu \\cdot \\sin(\\theta)}<br>]<\/p>\n\n\n\n<p>Substitute the known values:<\/p>\n\n\n\n<p>[<br>B = \\frac{1.33 \\times 10^{-5}}{(2.14 \\times 10^{-4}) \\cdot \\sin(31.5^\\circ)}<br>]<\/p>\n\n\n\n<p>First, calculate ( \\sin(31.5^\\circ) \\approx 0.523 ), and then:<\/p>\n\n\n\n<p>[<br>B = \\frac{1.33 \\times 10^{-5}}{(2.14 \\times 10^{-4}) \\cdot 0.523} \\approx 1.17 \\, \\text{T}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The strength of the magnetic field is approximately <strong>1.17 T<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A flat 145-turn current-carrying loop is immersed in a uniform magnetic field. The area of the loop is 6.75 cm2 and the angle between its magnetic dipole moment and the field is 31.5\u00b0. Find the strength of the magnetic field that causes a torque of 1.33 \u00d7 10-5 N\u00b7m to act on the loop when [&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-151919","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151919","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=151919"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151919\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=151919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=151919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=151919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}