{"id":27270,"date":"2025-06-19T21:52:42","date_gmt":"2025-06-19T21:52:42","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27270"},"modified":"2025-06-19T21:52:44","modified_gmt":"2025-06-19T21:52:44","slug":"the-additional-term-that-was-added-to-amperes-law-under-time-variation-represents-current-that-is-not-due-to-free-electrons-charge-flowing-directly-through-a-cross-sectional-surface","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-additional-term-that-was-added-to-amperes-law-under-time-variation-represents-current-that-is-not-due-to-free-electrons-charge-flowing-directly-through-a-cross-sectional-surface\/","title":{"rendered":"The additional term that was added to Ampere’s law under time variation represents current that is not due to free electrons (charge) flowing directly through a cross-sectional surface"},"content":{"rendered":"\n

The additional term that was added to Ampere’s law under time variation represents current that is not due to free electrons (charge) flowing directly through a cross-sectional surface. This current is called: A. None of these B. Free-electron current C. Displacement current D. Conduction current E. Convection current<\/p>\n\n\n\n

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

Correct Answer: C. Displacement current<\/strong><\/p>\n\n\n\n

Explanation (300 words):<\/h3>\n\n\n\n

In classical electromagnetism, Amp\u00e8re’s Law<\/strong> originally described the magnetic field generated by steady (unchanging) currents. However, James Clerk Maxwell recognized a critical limitation in the original form of this law. When applied to time-varying electric fields, such as those in a charging capacitor, Amp\u00e8re’s Law alone led to inconsistencies with the principle of charge conservation (continuity equation).<\/p>\n\n\n\n

To resolve this, Maxwell added an extra term<\/strong> to Amp\u00e8re\u2019s Law, introducing what is known as the displacement current<\/strong>. This term accounts for the changing electric field in regions where there is no actual movement of free charge (like between the plates of a capacitor).<\/p>\n\n\n\n

The modified form of Amp\u00e8re’s Law (one of Maxwell\u2019s equations) is: \u2207\u20d7\u00d7B\u20d7=\u03bc0J\u20d7+\u03bc0\u03b50\u2202E\u20d7\u2202t\\vec{\\nabla} \\times \\vec{B} = \\mu_0 \\vec{J} + \\mu_0\\varepsilon_0 \\frac{\\partial \\vec{E}}{\\partial t}<\/p>\n\n\n\n

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

    \n
  • B\u20d7\\vec{B} is the magnetic field,<\/li>\n\n\n\n
  • J\u20d7\\vec{J} is the conduction current density<\/strong> (due to actual moving charges),<\/li>\n\n\n\n
  • \u03b50\u2202E\u20d7\u2202t\\varepsilon_0 \\frac{\\partial \\vec{E}}{\\partial t} is the displacement current density<\/strong>,<\/li>\n\n\n\n
  • \u03bc0\\mu_0 is the permeability of free space,<\/li>\n\n\n\n
  • \u03b50\\varepsilon_0 is the permittivity of free space.<\/li>\n<\/ul>\n\n\n\n

    The displacement current<\/strong> is not a “real” current in the sense of flowing electrons; instead, it’s a mathematical term<\/strong> that represents the effect of a time-varying electric field<\/strong>. It allows the continuity of the magnetic field in places where there is no physical current, such as the space between capacitor plates during charging.<\/p>\n\n\n\n

    Summary:<\/h3>\n\n\n\n
      \n
    • Displacement current<\/strong> is the correct answer.<\/li>\n\n\n\n
    • It is essential for the consistency of Maxwell\u2019s equations.<\/li>\n\n\n\n
    • It enables electromagnetic waves to propagate in a vacuum, as in light.<\/li>\n<\/ul>\n\n\n\n

      Thus, option C: Displacement current<\/strong> is the correct and most complete answer.<\/p>\n","protected":false},"excerpt":{"rendered":"

      The additional term that was added to Ampere’s law under time variation represents current that is not due to free electrons (charge) flowing directly through a cross-sectional surface. This current is called: A. None of these B. Free-electron current C. Displacement current D. Conduction current E. Convection current The correct answer and explanation is: Correct […]<\/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-27270","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27270","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=27270"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27270\/revisions"}],"predecessor-version":[{"id":27271,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27270\/revisions\/27271"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27270"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27270"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27270"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}