Find magnetic flux density B circulation in closed contour

[Tegalad]

Homework Statement

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.

Homework Equations

∫B⋅dl=μ₀⋅I[/B]

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

 

[rude man]

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).