{"id":2640,"date":"2024-08-24T13:29:54","date_gmt":"2024-08-24T13:29:54","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2640"},"modified":"2024-08-24T13:29:54","modified_gmt":"2024-08-24T13:29:54","slug":"dynamically-induced-emf","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/24\/dynamically-induced-emf\/","title":{"rendered":"DYNAMICALLY INDUCED EMF"},"content":{"rendered":"\n

By either moving the conductor and keeping the magnetic field system stationary, or moving the field system and keeping the conductor stationary so that flux is cut by the conductor, the emf thus induced in the conductor is called dynamically induced emf.<\/em><\/p>\n\n\n\n

<\/a>5.18.1  Mathematical Expression<\/h4>\n\n\n\n

Considering a conductor of length\u00a0l<\/em>\u00a0m placed in the magnetic field of flux density\u00a0B<\/em>\u00a0Wb\/m2<\/sup>\u00a0is moving at right angle to the field at a velocity\u00a0v<\/em>\u00a0m\/s, as shown in\u00a0Figure 5.29(a). Let the conductor be moved through a small distance\u00a0dx<\/em>\u00a0m in time\u00a0dt<\/em>\u00a0s, as shown in\u00a0Figure 5.29 (b).<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 5.29<\/strong>  Dynamically induced emf (a) Conductor moves perpendicular to the magnetic field (b) Distance covered (dx) (c) Area swept (d) Conductor moves at an angle \u03b8<\/em><\/strong> with the direction of magnetic field<\/p>\n\n\n\n

Area swept by the conductor, A<\/em> = l<\/em> \u00d7 dx<\/em><\/p>\n\n\n\n

Flux cut by the conductor, \u0278<\/em> = B<\/em> \u00d7 A<\/em> = Bldx<\/em><\/p>\n\n\n\n

According to Faraday\u2019s Law of electromagnetic induction;<\/p>\n\n\n\n

Induced emf, \"image\"<\/p>\n\n\n\n

Now, if the conductor is moved at an angle\u00a0\u03b8<\/em>\u00a0with the direction of magnetic field at a velocity \u03c5 m\/s, as shown in\u00a0Figure 5.29(d). A small distance covered by the conductor in that direction is\u00a0dx<\/em>\u00a0in time\u00a0dt<\/em>\u00a0s. Then, the component of distance perpendicular to the magnetic field, which produces emf, is\u00a0dx<\/em>\u00a0sin\u00a0\u03b8<\/em>.<\/p>\n\n\n\n

Therefore, area swept by the conductor, A<\/em> = l<\/em> \u00d7 dx<\/em> sin \u03b8<\/em><\/p>\n\n\n\n

Flux cut by the conductor, \u0278<\/em> = B<\/em> \u00d7 A<\/em> = Bldx<\/em>sin \u03b8<\/em><\/p>\n\n\n\n

Induced emf, \"image\"<\/p>\n\n\n\n

Example 5.21<\/strong><\/p>\n\n\n\n

A coil of 500 turns is linked with a flux of 2 mWb. If this flux is reversed in 4 ms, calculate the average emf induced in the coil.<\/p>\n\n\n\n

Solution:<\/em><\/p>\n\n\n\n

Average induced emf, \"image\"<\/p>\n\n\n\n

where N<\/em> = 500 turns; d<\/em>\u0278<\/em> = 2 \u2212 (\u2212 2) = 4 mWb; dt<\/em> = 4 \u00d7 103<\/sup> s<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

<\/a>Example 5.22<\/strong><\/p>\n\n\n\n

A coil of 250 turns is wound on a magnetic circuit of reluctance 100,000 AT\/Wb. If a current of 2 A flowing in the coil is reversed in 5 ms, find the average emf induced in the coil.<\/p>\n\n\n\n

Solution:<\/em><\/p>\n\n\n\n

\u0278<\/em> = mmf\/reluctance, that is, \u0278<\/em> = NI<\/em>\/S<\/em><\/p>\n\n\n\n

where N<\/em> = 250, I<\/em> = 2 A, and S<\/em> = 100,000 AT\/Wb<\/p>\n\n\n\n

\u2234<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Average induced emf, \"image\"<\/p>\n\n\n\n

where d<\/em>\u0278<\/em> = 5 \u2212 (\u2212 5) = 10 mWb (since current is reversed)<\/p>\n\n\n\n

\"image\"\/<\/figure>\n","protected":false},"excerpt":{"rendered":"

By either moving the conductor and keeping the magnetic field system stationary, or moving the field system and keeping the conductor stationary so that flux is cut by the conductor, the emf thus induced in the conductor is called dynamically induced emf. 5.18.1  Mathematical Expression Considering a conductor of length\u00a0l\u00a0m placed in the magnetic field of flux […]<\/p>\n","protected":false},"author":1,"featured_media":2479,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[407],"tags":[],"class_list":["post-2640","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-magnetic-circuits"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/magnet_1653038-1.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2640","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2640"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2640\/revisions"}],"predecessor-version":[{"id":2641,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2640\/revisions\/2641"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2479"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2640"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}