{"id":43642,"date":"2025-06-30T08:46:52","date_gmt":"2025-06-30T08:46:52","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=43642"},"modified":"2025-06-30T08:46:57","modified_gmt":"2025-06-30T08:46:57","slug":"two-infinite-conductors-are-placed-parallel-to-each-other-2-cm-apart-and-presenting-each-one-of-them-a-current-of-2-a","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/two-infinite-conductors-are-placed-parallel-to-each-other-2-cm-apart-and-presenting-each-one-of-them-a-current-of-2-a\/","title":{"rendered":"Two infinite conductors are placed parallel to each other, 2 cm apart and presenting each one of them a current of 2 A"},"content":{"rendered":"\n

Two infinite conductors are placed parallel to each other, 2 cm apart and presenting each one of them a current of 2 A. A) Draw the problem with the corresponding forces and magnetic fields. B) Calculate the force magnitude experienced by these two conductors.<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

A) Diagram of the Problem<\/h3>\n\n\n\n
    \n
  1. Two parallel conductors are placed 2 cm apart.<\/li>\n\n\n\n
  2. Each conductor carries a current of 2 A.<\/li>\n\n\n\n
  3. The magnetic field generated by one conductor exerts a force on the other conductor due to the interaction of their magnetic fields.<\/li>\n<\/ol>\n\n\n\n

    The conductors will create a magnetic field around them due to the current flowing through them. The magnetic field from one conductor interacts with the current in the second conductor, resulting in a force.<\/p>\n\n\n\n

      \n
    • The magnetic field BB around each conductor is generated by Amp\u00e8re’s Law and points in concentric circles around the wire.<\/li>\n\n\n\n
    • If the currents are in the same direction, the magnetic fields will interact in such a way that the two wires will experience an attractive force.<\/li>\n\n\n\n
    • If the currents are in opposite directions, the force between the wires will be repulsive.<\/li>\n<\/ul>\n\n\n\n

      B) Calculation of the Force Magnitude<\/h3>\n\n\n\n

      To calculate the force between two parallel conductors, we use Amp\u00e8re\u2019s force law. The formula for the force per unit length between two parallel conductors is: F=\u03bc0I1I22\u03c0dF = \\frac{{\\mu_0 I_1 I_2}}{{2 \\pi d}}<\/p>\n\n\n\n

      Where:<\/p>\n\n\n\n

        \n
      • FF is the force per unit length,<\/li>\n\n\n\n
      • \u03bc0=4\u03c0\u00d710\u22127\u2009T\\cdotpm\/A\\mu_0 = 4 \\pi \\times 10^{-7} \\, \\text{T\u00b7m\/A} is the permeability of free space,<\/li>\n\n\n\n
      • I1I_1 and I2I_2 are the currents in the two conductors (both 2 A),<\/li>\n\n\n\n
      • d=2\u2009cm=0.02\u2009md = 2 \\, \\text{cm} = 0.02 \\, \\text{m} is the distance between the conductors.<\/li>\n<\/ul>\n\n\n\n

        Substituting the given values: F=(4\u03c0\u00d710\u22127)\u00d7(2)\u00d7(2)2\u03c0\u00d70.02F = \\frac{{(4 \\pi \\times 10^{-7}) \\times (2) \\times (2)}}{{2 \\pi \\times 0.02}}<\/p>\n\n\n\n

        Simplifying: F=16\u03c0\u00d710\u221272\u03c0\u00d70.02=8\u00d710\u221270.02=4\u00d710\u22125\u2009N\/mF = \\frac{{16 \\pi \\times 10^{-7}}}{{2 \\pi \\times 0.02}} = \\frac{{8 \\times 10^{-7}}}{{0.02}} = 4 \\times 10^{-5} \\, \\text{N\/m}<\/p>\n\n\n\n

        Thus, the force per unit length between the two conductors is 4\u00d710\u22125\u2009N\/m4 \\times 10^{-5} \\, \\text{N\/m}.<\/p>\n\n\n\n

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

        The force experienced by each conductor due to the magnetic field of the other is 4\u00d710\u22125\u2009N\/m4 \\times 10^{-5} \\, \\text{N\/m}. If the currents flow in the same direction, the force will be attractive; if they flow in opposite directions, the force will be repulsive.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Two infinite conductors are placed parallel to each other, 2 cm apart and presenting each one of them a current of 2 A. A) Draw the problem with the corresponding forces and magnetic fields. B) Calculate the force magnitude experienced by these two conductors. The correct answer and explanation is: A) Diagram of the Problem […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-43642","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43642","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=43642"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43642\/revisions"}],"predecessor-version":[{"id":43643,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43642\/revisions\/43643"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=43642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=43642"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=43642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}