{"id":145490,"date":"2024-09-27T09:49:21","date_gmt":"2024-09-27T09:49:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=145490"},"modified":"2024-09-27T09:49:23","modified_gmt":"2024-09-27T09:49:23","slug":"two-long-parallel-wires-carry-currents-of-10-a-in-opposite-directions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/27\/two-long-parallel-wires-carry-currents-of-10-a-in-opposite-directions\/","title":{"rendered":"Two long parallel wires carry currents of 10 A in opposite directions"},"content":{"rendered":"\n<p>Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other<\/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 find the magnetic field in the plane of two long parallel wires carrying currents of 10 A in opposite directions, we can use the formula for the magnetic field due to a long straight wire:<\/p>\n\n\n\n<p>[<br>B = \\frac{\\mu_0 I}{2 \\pi r}<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,<\/li>\n\n\n\n<li>( \\mu_0 ) is the permeability of free space (( 4\\pi \\times 10^{-7} \\, \\text{T m\/A} )),<\/li>\n\n\n\n<li>( I ) is the current in the wire (10 A in this case),<\/li>\n\n\n\n<li>( r ) is the distance from the wire to the point where the magnetic field is being calculated.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Current ( I = 10 \\, \\text{A} )<\/li>\n\n\n\n<li>Distance between the wires = 40 cm = 0.4 m<\/li>\n\n\n\n<li>Distance from the first wire (wire 1) to the point = 20 cm = 0.2 m<\/li>\n\n\n\n<li>Distance from the second wire (wire 2) to the point = 60 cm = 0.6 m<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the magnetic field due to each wire at the point of interest.<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>For Wire 1 (current flowing in one direction)<\/strong>:<br>[<br>B_1 = \\frac{\\mu_0 \\cdot 10 \\, \\text{A}}{2 \\pi \\cdot 0.2 \\, \\text{m}} = \\frac{4\\pi \\times 10^{-7} \\cdot 10}{2 \\pi \\cdot 0.2} = \\frac{2 \\times 10^{-6}}{0.2} = 1 \\times 10^{-5} \\, \\text{T}<br>]<br>The direction of this magnetic field (using the right-hand rule) will be into the page.<\/li>\n\n\n\n<li><strong>For Wire 2 (current flowing in the opposite direction)<\/strong>:<br>[<br>B_2 = \\frac{\\mu_0 \\cdot 10 \\, \\text{A}}{2 \\pi \\cdot 0.6 \\, \\text{m}} = \\frac{4\\pi \\times 10^{-7} \\cdot 10}{2 \\pi \\cdot 0.6} = \\frac{2 \\times 10^{-6}}{0.6} = \\frac{1}{3} \\times 10^{-6} \\, \\text{T} \\approx 0.6667 \\times 10^{-6} \\, \\text{T}<br>]<br>The direction of this magnetic field will be out of the page.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine the net magnetic field at the point.<\/h3>\n\n\n\n<p>Since ( B_1 ) is directed into the page and ( B_2 ) is directed out of the page, they will oppose each other:<\/p>\n\n\n\n<p>[<br>B_{\\text{net}} = B_1 &#8211; B_2 = 1 \\times 10^{-5} \\, \\text{T} &#8211; 0.6667 \\times 10^{-6} \\, \\text{T} = 0.9333 \\times 10^{-5} \\, \\text{T} \\approx 9.33 \\times 10^{-6} \\, \\text{T}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The net magnetic field at the point 20 cm from one wire and 60 cm from the other wire is approximately ( 9.33 \\times 10^{-6} \\, \\text{T} ), directed into the page. This result highlights how magnetic fields interact and reinforce or cancel based on the direction of current flow in parallel conductors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other The Correct Answer and Explanation is : To find the [&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-145490","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145490","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=145490"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145490\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145490"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145490"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}