{"id":149279,"date":"2024-03-04T18:07:10","date_gmt":"2024-03-04T12:37:10","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=149279"},"modified":"2024-03-04T18:07:10","modified_gmt":"2024-03-04T12:37:10","slug":"define-mutual-inductance-write-its-si-unit-derive-an-expression-for","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/define-mutual-inductance-write-its-si-unit-derive-an-expression-for","title":{"rendered":"Define mutual inductance. Write its SI unit. Derive an expression for…"},"content":{"rendered":"

(i) Define mutual inductance. Write its SI unit.
\n(ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length l, having turns N, and N, and of radi r, and re (> r,).<\/h2>\n

Ans.<\/h3>\n
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(i) Mutual inductance (\ufffd<\/span>M<\/span><\/span><\/span><\/span><\/span>) is a measure of how much one coil induces an electromotive force (emf) in another coil when the current in the first coil changes. It is measured in henries (H).<\/h3>\n

(ii) The expression for the mutual inductance (\ufffd<\/span>M<\/span><\/span><\/span><\/span><\/span>) of a system of two long coaxial solenoids of the same length \ufffd<\/span>l<\/span><\/span><\/span><\/span><\/span>, having \ufffd1<\/span>N<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and \ufffd2<\/span>N<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> turns, and radii \ufffd1<\/span>r<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and \ufffd2<\/span>r<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (\ufffd2>\ufffd1<\/span>r<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>><\/span><\/span>r<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) is:<\/h3>\n

\ufffd=\ufffd0\ufffd1\ufffd2\ufffd2\ufffd<\/span>M<\/span>=<\/span><\/span>l<\/span><\/span><\/span>\u03bc<\/span>0<\/span>\u200b<\/span><\/span>N<\/span>1<\/span>\u200b<\/span><\/span>N<\/span>2<\/span>\u200b<\/span><\/span>A<\/span>2<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

where:<\/h3>\n
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    \ufffd0<\/span>\u03bc<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the permeability of free space,<\/h3>\n<\/li>\n
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    \ufffd1<\/span>N<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and \ufffd2<\/span>N<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> are the number of turns in the solenoids,<\/h3>\n<\/li>\n
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    \ufffd2<\/span>A<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the cross-sectional area of solenoid 2,<\/h3>\n<\/li>\n
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    \ufffd<\/span>l<\/span><\/span><\/span><\/span><\/span> is the length of the solenoids.<\/h3>\n<\/li>\n<\/ul>\n

    This expression represents the mutual inductance between the two solenoids in the given configuration.<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    (i) Define mutual inductance. Write its SI unit. (ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length l, having turns N, and N, and of radi r, and re (> r,). Ans. (i) Mutual inductance (\ufffdM) is a measure of how much one coil induces […]<\/p>\n","protected":false},"author":21830,"featured_media":114041,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-149279","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/149279","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21830"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=149279"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/149279\/revisions"}],"predecessor-version":[{"id":149280,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/149279\/revisions\/149280"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/114041"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=149279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=149279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=149279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}