Chapter One: Vector Analysis The use of vectors and vector analysis ...

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Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department So the total flux is: ∙ 8 162448 The Fundamental Theorem for Curls: The fundamental theorem of Curls, which goes by the special name of Stokes’ theorem state that: ∙ V As always, the integral of a derivative (here, the curl) over a region (here, a patch of surface) is equal to value of the function at the boundary (here, the perimeter of the patch). ∙ If your finger point in the direction of the line integral, then your thumb fixed the direction of . Corollary(1): ∙ depends only on the boundary line, not on the particular surface used. Corollary(2): ∮ ∙ 0 for any closed surface. Example: Suppose 2 3 4 Check Stokes’ theorem for the square surface in Fig.
Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department The Stokes’ theorem state that: ∙ V ∙ ∵ 0 4 2 2 ⟹ ∙ 4 2 ∙ 4 3 ⟹ ∙ 4 Breaking the line integral into four segments: (i) 0 ; 0 ; ∙ 3 (ii) 0 ; 1 ; ∙ 4 (iii) 0 (iv) ; 1 ; ∙ 3 0 ; 0 ; ∙ 0 ⟹ ⟹ ⟹ ⟹ ∙ 3 1 ∙ 4 4 3 ∙ 3 1 ∙ 0 0
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Chapter One: Vector Analysis The use of vectors and vector analysis ...

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