Nonnuclear submarines use batteries for power when submerged.
Find the magnetic field 55 cm from a straight wire carrying 1150 A from the batteries to the drive mechanism of a submarine.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The magnetic field a distance rr from a long, straight current\u2011carrying conductor is given by Amp\u00e8re\u2019s law (or the Biot\u2013Savart law in its simplified form for straight wires): B=\u03bc0I2\u03c0rB = \\frac{\\mu_0 I}{2\\pi r}<\/p>\n\n\n\n where<\/p>\n\n\n\n For I=1150 AI = 1150\\ \\mathrm{A} and r=0.55 mr = 0.55\\ \\mathrm{m}: B=(4\u03c0\u00d710\u22127\u2009T\u22c5m\/A)\u00d71150 A2\u03c0\u00d70.55 m=4\u03c0\u00d710\u22127\u00d711502\u03c0\u00d70.55 T=2\u00d71150\u00d710\u221270.55 T=2.30\u00d710\u221240.55 T\u22484.18\u00d710\u22124 T.\\begin{aligned} B &= \\frac{(4\\pi\\times10^{-7}\\,\\mathrm{T\\cdot m\/A}) \\times 1150\\ \\mathrm{A}}{2\\pi \\times 0.55\\ \\mathrm{m}} \\\\[6pt] &= \\frac{4\\pi\\times10^{-7} \\times 1150}{2\\pi \\times 0.55}\\ \\mathrm{T} \\\\[6pt] &= \\frac{2 \\times 1150 \\times 10^{-7}}{0.55}\\ \\mathrm{T} \\\\[6pt] &= \\frac{2.30 \\times 10^{-4}}{0.55}\\ \\mathrm{T} \\\\[6pt] &\\approx 4.18\\times10^{-4}\\ \\mathrm{T}. \\end{aligned}<\/p>\n\n\n\n Thus B\u22484.18\u00d710\u22124 tesla=418 \u03bcT.\\boxed{B \\approx 4.18\\times10^{-4}\\ \\text{tesla} = 418\\ \\mu\\text{T}.}<\/p>\n\n\n\n Answer:<\/strong> B\u22484.18\u00d710\u22124 TB \\approx 4.18\\times10^{-4}\\ \\mathrm{T}<\/p>\n","protected":false},"excerpt":{"rendered":" Nonnuclear submarines use batteries for power when submerged.Find the magnetic field 55 cm from a straight wire carrying 1150 A from the batteries to the drive mechanism of a submarine. The Correct Answer and Explanation is: The magnetic field a distance rr from a long, straight current\u2011carrying conductor is given by Amp\u00e8re\u2019s law (or the […]<\/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-216631","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216631","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=216631"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216631\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=216631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=216631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=216631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n\n\n\nCalculation<\/h3>\n\n\n\n
\n\n\n\nExplanation and Context<\/h3>\n\n\n\n
\n
Amp\u00e8re\u2019s law in integral form states \u222eB\u22c5d\u2113=\u03bc0Ienc\\displaystyle \\oint \\mathbf{B}\\cdot d\\boldsymbol\\ell = \\mu_0 I_{\\rm enc}. For a circular path of radius rr concentric with a straight wire, B\\mathbf{B} is tangent and constant in magnitude, so B(2\u03c0r)=\u03bc0IB (2\\pi r)=\\mu_0 I, yielding the formula above.<\/li>\n\n\n\n
In non\u2011nuclear submarines, high\u2011capacity batteries supply large currents (on the order of 10\u00b3 A) to electric motors that drive the propellers when submerged. The returning current through the hull or dedicated return conductor thus generates magnetic fields in the vicinity of these power cables.<\/li>\n\n\n\n
A field of 4.18\u00d710\u22124\u2009T4.18\\times10^{-4}\\,\\mathrm{T} is about 7\u20138 times stronger than Earth\u2019s magnetic field (~50\u202f\u03bcT). In submarine stealth considerations, such local magnetic anomalies can be detected by magnetic anomaly detectors (MAD) in anti\u2011submarine aircraft, so power\u2011cable routing and magnetic signature reduction techniques (e.g., degaussing coils) are critical.<\/li>\n\n\n\n
The magnetic field lines circle the wire according to the right\u2011hand rule: if the thumb points in the direction of current flow, the curled fingers show the sense of B\\mathbf{B}. At a point fixed relative to the wire, reversing the current reverses the field direction.<\/li>\n\n\n\n
Note the 1\/r1\/r dependence: doubling the distance to 1.10\u00a0m1.10\\ \\mathrm{m} would halve the field to \u223c2.09\u00d710\u22124\u2009T\\sim2.09\\times10^{-4}\\,\\mathrm{T}. This rapid spatial decay underscores why shielding and physical separation can mitigate stray magnetic fields in sensitive onboard equipment.<\/li>\n<\/ol>\n\n\n\n
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