{"id":160469,"date":"2024-11-03T04:38:02","date_gmt":"2024-11-03T04:38:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=160469"},"modified":"2024-11-03T04:38:05","modified_gmt":"2024-11-03T04:38:05","slug":"a-rectangular-loop-of-wire-with-sides-h26cm-and-w65cm-is-located-in-a-region-containing-a-constant-magnetic-field-b1-12t-that-is-aligned-with-the-positive-y-axis","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/03\/a-rectangular-loop-of-wire-with-sides-h26cm-and-w65cm-is-located-in-a-region-containing-a-constant-magnetic-field-b1-12t-that-is-aligned-with-the-positive-y-axis\/","title":{"rendered":"A rectangular loop of wire with sides H=26cm and W=65cm is located in a region containing a constant magnetic field B=1.12T that is aligned with the positive y-axis"},"content":{"rendered":"\n

A rectangular loop of wire with sides H=26cm and W=65cm is located in a region containing a constant magnetic field B=1.12T that is aligned with the positive y-axis. The loop carries a current I=205mA . The plane of the loop is inclined at an angle \u03b8=28
\u2218
with respect to the x-axis.<\/p>\n\n\n\n

    \n
  1. What is \u03bc
    x
    \u200b
    , the x-component of the magnetic moment vector of the loop? 2. What is \u03bc
    y
    \u200b
    , the y-component of the magnetic moment vector of the loop? 3. What is \u03c4
    z
    \u200b
    , the z-component of the torque exerted on the loop? 4. What is F
    bc
    \u200b
    , the magnitude of the force exerted on segment bc of the loop? 5. What is the direction of the force that is exerted on segment bc of the loop? – A. Along the negative x-direction – B. Along the negative y-direction – C. Along the positive x-direction – D. Along the positive y-direction – E. None of the above<\/li>\n<\/ol>\n\n\n\n

    The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

    To analyze the rectangular loop of wire carrying a current in a magnetic field, we can derive the necessary quantities step by step.<\/p>\n\n\n\n

    1. Magnetic Moment ( \\mu_x )<\/h3>\n\n\n\n

    The magnetic moment ( \\mu ) of a rectangular loop is given by the formula:
    [
    \\mu = I \\cdot A
    ]
    where ( I ) is the current and ( A ) is the area of the loop. The area ( A ) can be calculated as:
    [
    A = H \\times W = 0.26 \\, \\text{m} \\times 0.65 \\, \\text{m} = 0.169 \\, \\text{m}^2
    ]<\/p>\n\n\n\n

    Thus,
    [
    \\mu = 0.205 \\, \\text{A} \\times 0.169 \\, \\text{m}^2 = 0.034645 \\, \\text{A} \\cdot \\text{m}^2
    ]<\/p>\n\n\n\n

    Since the loop is inclined at an angle ( \\theta ) with respect to the x-axis, we can find the components:
    [
    \\mu_x = \\mu \\cdot \\cos(\\theta) = 0.034645 \\cdot \\cos(28^\\circ) \\approx 0.0306 \\, \\text{A} \\cdot \\text{m}^2
    ]<\/p>\n\n\n\n

    2. Magnetic Moment ( \\mu_y )<\/h3>\n\n\n\n

    [
    \\mu_y = \\mu \\cdot \\sin(\\theta) = 0.034645 \\cdot \\sin(28^\\circ) \\approx 0.0164 \\, \\text{A} \\cdot \\text{m}^2
    ]<\/p>\n\n\n\n

    3. Torque ( \\tau_z )<\/h3>\n\n\n\n

    The torque ( \\tau ) exerted on a magnetic moment in a magnetic field is given by:
    [
    \\tau = \\mu \\times B
    ]
    The magnitude of the torque about the z-axis can be calculated using:
    [
    \\tau_z = \\mu \\cdot B \\cdot \\sin(\\theta) = 0.034645 \\cdot 1.12 \\cdot \\sin(28^\\circ) \\approx 0.01065 \\, \\text{N} \\cdot \\text{m}
    ]<\/p>\n\n\n\n

    4. Force on Segment ( bc ) (( F_{bc} ))<\/h3>\n\n\n\n

    The force on a current-carrying segment in a magnetic field is given by:
    [
    F = I \\cdot L \\times B
    ]
    Where ( L ) is the length of the segment and points in the direction of the current. The length of segment ( bc ) is ( H = 0.26 \\, \\text{m} ), and since it is aligned along the width in the x-direction, the force is:
    [
    F_{bc} = I \\cdot H \\cdot B = 0.205 \\cdot 0.26 \\cdot 1.12 \\approx 0.059 \\, \\text{N}
    ]<\/p>\n\n\n\n

    5. Direction of the Force<\/h3>\n\n\n\n

    Using the right-hand rule, since the current ( I ) flows upward in the y-direction (the direction of the magnetic field) and the magnetic field is along the positive y-axis, the force on segment ( bc ) will be directed along the negative x-direction. Thus, the correct answer is:<\/p>\n\n\n\n

      \n
    • A. Along the negative x-direction<\/strong><\/li>\n<\/ul>\n\n\n\n

      Conclusion<\/h3>\n\n\n\n

      This analysis of the magnetic properties of a rectangular loop in a magnetic field highlights the importance of understanding the relationships between current, magnetic fields, and forces acting on current-carrying conductors. Each step provides insight into how the geometry and orientation of the loop impact the magnetic moment and resulting forces, making this a fundamental topic in electromagnetism.<\/p>\n","protected":false},"excerpt":{"rendered":"

      A rectangular loop of wire with sides H=26cm and W=65cm is located in a region containing a constant magnetic field B=1.12T that is aligned with the positive y-axis. The loop carries a current I=205mA . The plane of the loop is inclined at an angle \u03b8=28\u2218with respect to the x-axis. The Correct Answer and Explanation […]<\/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-160469","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160469","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=160469"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160469\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160469"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160469"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}