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Find magnetic flux density B circulation in closed contour

  1. Dec 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Find magnetic flux density B circulation in closed contour. The countour consists of square with a perimeter of 4b. It includes a square conductor with a perimeter of 4a. A homogenic current flows through a conductor with a current density of j.
    kIPvEOH.png

    2. Relevant equations
    ∫B⋅dl=μ0⋅I


    3. The attempt at a solution
    I get this equation ∫B⋅dl=μ0⋅j⋅a2 but the answer says that the integration contour is Γ. How do I get the Γ? ΓB⋅dl=μ0⋅j⋅a2
     
  2. jcsd
  3. Dec 16, 2016 #2

    rude man

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    Homework Helper
    Gold Member

    Well, since it's been nearly 120 hrs (5 days) with no other posters,I will suggest:
    (1) line integral of H over ANY section of the large perimeter WITH ZERO CURRENT EVERYWHERE = 0. This includes the two "a" sections common to the large & small perimeters.
    (2) line integral over any one of the four current-carrying section sides (by Ampere's law) = ja2(a) = ja3.
    (3) Thus the circulation of H over the two common "a" sections = 2ja3 and of course B = μ0H.
    (4) Add (3) to (1) and you get the answer of (3).
     
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