{"id":88500,"date":"2025-06-01T07:12:23","date_gmt":"2025-06-01T07:12:23","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88500"},"modified":"2025-06-01T07:12:23","modified_gmt":"2025-06-01T07:12:23","slug":"a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/","title":{"rendered":"A circular coil of radius R having N number of turns carries a steady"},"content":{"rendered":"<p>A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0\u00b71 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?<\/p>\n<p>[amp_mcq option1=&#8221;0\u00b705 tesla&#8221; option2=&#8221;0\u00b72 tesla&#8221; option3=&#8221;0\u00b74 tesla&#8221; option4=&#8221;0\u00b78 tesla&#8221; correct=&#8221;option3&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC NDA-2 &#8211; 2018<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-nda-2-2018.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-nda-2-2018\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nThe correct value for the magnetic induction at the centre of the coil will be 0.4 tesla.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\nThe magnetic field (B) at the centre of a circular coil is given by the formula $B = (\\mu_0 N I) \/ (2R)$, where $\\mu_0$ is the permeability of free space, N is the number of turns, I is the current, and R is the radius of the coil.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nInitially, $B_1 = (\\mu_0 N_1 I_1) \/ (2R_1) = 0.1$ T. Let $N_1=N$, $R_1=R$, $I_1=I$.<br \/>\nSo, $0.1 = (\\mu_0 N I) \/ (2R)$.<br \/>\nIn the new scenario, the number of turns is doubled ($N_2 = 2N$) and the radius is halved ($R_2 = R\/2$), while the current remains steady ($I_2 = I$).<br \/>\nThe new magnetic field $B_2$ is given by:<br \/>\n$B_2 = (\\mu_0 N_2 I_2) \/ (2R_2) = (\\mu_0 (2N) I) \/ (2(R\/2)) = (\\mu_0 2N I) \/ R$.<br \/>\nWe can express $B_2$ in terms of $B_1$:<br \/>\n$B_2 = (\\mu_0 2N I) \/ R = 4 \\times (\\mu_0 N I) \/ (2R) = 4 \\times B_1$.<br \/>\nSubstituting the value of $B_1$:<br \/>\n$B_2 = 4 \\times 0.1$ T = 0.4 T.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0\u00b71 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"A circular coil of radius R having N number of turns carries a steady\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/#more-88500\">Detailed Solution<span class=\"screen-reader-text\">A circular coil of radius R having N number of turns carries a steady<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1094],"tags":[1114,1201,1128],"class_list":["post-88500","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1114","tag-electric-current","tag-physics","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A circular coil of radius R having N number of turns carries a steady<\/title>\n<meta name=\"description\" content=\"The correct value for the magnetic induction at the centre of the coil will be 0.4 tesla. The magnetic field (B) at the centre of a circular coil is given by the formula $B = (mu_0 N I) \/ (2R)$, where $mu_0$ is the permeability of free space, N is the number of turns, I is the current, and R is the radius of the coil.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A circular coil of radius R having N number of turns carries a steady\" \/>\n<meta property=\"og:description\" content=\"The correct value for the magnetic induction at the centre of the coil will be 0.4 tesla. The magnetic field (B) at the centre of a circular coil is given by the formula $B = (mu_0 N I) \/ (2R)$, where $mu_0$ is the permeability of free space, N is the number of turns, I is the current, and R is the radius of the coil.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:12:23+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A circular coil of radius R having N number of turns carries a steady","description":"The correct value for the magnetic induction at the centre of the coil will be 0.4 tesla. The magnetic field (B) at the centre of a circular coil is given by the formula $B = (mu_0 N I) \/ (2R)$, where $mu_0$ is the permeability of free space, N is the number of turns, I is the current, and R is the radius of the coil.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/","og_locale":"en_US","og_type":"article","og_title":"A circular coil of radius R having N number of turns carries a steady","og_description":"The correct value for the magnetic induction at the centre of the coil will be 0.4 tesla. The magnetic field (B) at the centre of a circular coil is given by the formula $B = (mu_0 N I) \/ (2R)$, where $mu_0$ is the permeability of free space, N is the number of turns, I is the current, and R is the radius of the coil.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:12:23+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/","name":"A circular coil of radius R having N number of turns carries a steady","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:12:23+00:00","dateModified":"2025-06-01T07:12:23+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct value for the magnetic induction at the centre of the coil will be 0.4 tesla. The magnetic field (B) at the centre of a circular coil is given by the formula $B = (\\mu_0 N I) \/ (2R)$, where $\\mu_0$ is the permeability of free space, N is the number of turns, I is the current, and R is the radius of the coil.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-coil-of-radius-r-having-n-number-of-turns-carries-a-steady\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-2\/"},{"@type":"ListItem","position":3,"name":"A circular coil of radius R having N number of turns carries a steady"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88500","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=88500"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88500\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}