{"id":131183,"date":"2023-02-15T12:23:37","date_gmt":"2023-02-15T06:53:37","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=131183"},"modified":"2023-02-15T12:23:37","modified_gmt":"2023-02-15T06:53:37","slug":"two-long-straight-parallel-conductors-carrying-currents-i1-and-i2-are-separated-by-a-distance-d","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/education\/two-long-straight-parallel-conductors-carrying-currents-i1-and-i2-are-separated-by-a-distance-d","title":{"rendered":"Two long straight parallel conductors carrying currents I1 and I2 are separated by a distance d&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;"},"content":{"rendered":"<h2>Question 10:Two long straight parallel conductors carrying currents I1 and I2 are separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field produced by one exerts an<br \/>\nattractive force on the other. Obtain the expression for this force and hence define 1 ampere.<\/h2>\n<h3>The correct answer is &#8211; The magnetic field produced by a long straight conductor carrying a current I at a distance r from the conductor is given by:<\/h3>\n<div class=\"w-full border-b border-black\/10 dark:border-gray-900\/50 text-gray-800 dark:text-gray-100 group bg-gray-50 dark:bg-[#444654]\">\n<div class=\"text-base gap-4 md:gap-6 m-auto md:max-w-2xl lg:max-w-2xl xl:max-w-3xl p-4 md:py-6 flex lg:px-0\">\n<div class=\"relative flex w-[calc(100%-50px)] flex-col gap-1 md:gap-3 lg:w-[calc(100%-115px)]\">\n<div class=\"flex flex-grow flex-col gap-3\">\n<div class=\"min-h-[20px] flex flex-col items-start gap-4 whitespace-pre-wrap\">\n<div class=\"markdown prose w-full break-words dark:prose-invert dark\">\n<h3>B = \u03bc0I \/ (2\u03c0r)<\/h3>\n<h3>where \u03bc0 is the permeability of free space.<\/h3>\n<h3>In the case of two long straight parallel conductors carrying currents I1 and I2 and separated by a distance d, the magnetic field produced by conductor 1 at a point on conductor 2 is given by:<\/h3>\n<h3>B1 = \u03bc0I1 \/ (2\u03c0d)<\/h3>\n<h3>Since the currents are flowing in the same direction, the magnetic field produced by conductor 1 is in the same direction as the magnetic field produced by conductor 2.<\/h3>\n<h3>According to the right-hand rule, the direction of the force on a current-carrying conductor in a magnetic field is perpendicular to both the direction of the current and the direction of the magnetic field. In this case, the force on conductor 2 due to the magnetic field produced by conductor 1 is perpendicular to both the magnetic field and the direction of the current in conductor 2, and is attractive.<\/h3>\n<h3>The magnitude of the force F on conductor 2 due to the magnetic field produced by conductor 1 can be obtained using the formula:<\/h3>\n<h3>F = I2LB1<\/h3>\n<h3>where L is the length of the conductor 2 that is in the magnetic field of conductor 1.<\/h3>\n<h3>Assuming that conductor 2 is also a long straight conductor of length L and is at a distance r from conductor 1, we can express L in terms of d and r as:<\/h3>\n<h3>L = \u221a(d^2 + r^2)<\/h3>\n<h3>Substituting the expression for B1 and L, we get:<\/h3>\n<h3>F = I2LB1 = I2L(\u03bc0I1 \/ 2\u03c0d) = I1I2L\u03bc0 \/ 2\u03c0d<\/h3>\n<h3>Substituting the expression for L, we get:<\/h3>\n<h3>F = I1I2\u221a(d^2 + r^2)\u03bc0 \/ 2\u03c0d<\/h3>\n<h3>This is the expression for the force on conductor 2 due to the magnetic field produced by conductor 1.<\/h3>\n<h3>One ampere (1 A) is defined as the current that produces a force of 2 \u00d7 10^-7 newtons per meter of length when two long straight parallel conductors of negligible cross-sectional area are separated by a distance of 1 meter and carry currents of 1 ampere each.<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Question 10:Two long straight parallel conductors carrying currents I1 and I2 are separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field produced by one exerts an attractive force on the other. Obtain the expression for this force and hence define 1 ampere. The correct answer [&hellip;]<\/p>\n","protected":false},"author":21830,"featured_media":131018,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":{"0":"post-131183","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-education"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/131183","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=131183"}],"version-history":[{"count":2,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/131183\/revisions"}],"predecessor-version":[{"id":131187,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/131183\/revisions\/131187"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/131018"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=131183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=131183"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=131183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}