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 (ii) 2 ; 0 ⟹ T∙ 2 4 T∙ 4 2 1 0 2 We have 20 2 If we tack the path (iii): ⟹ ⟹ T∙ 2 T∙ 2 The Fundamental Theorem for Divergences: The fundamental theorem for divergences state that: ∙ V ∙ This theorem has at least three special names: Gauss’s theorem , Green’s theorem , or, simply, the Divergence theorem. It say that the integral of a derivative (in this case the divergence) over a region (in this case a volume) is equal to the value of the function at the boundary (in this case the surface) that bounds the volume. Example: Check the divergencee theorem using the function: 2 2 and the unit cube situated at the origin. Solution:
Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department The fundamental theorem for divergences state that: (i) ∙ V ∙ ∙ 2 ∙ 2 2 ⟹ ∴ ∙ 2 1 ⟹ 1 1 (ii) (iii) (iv) (v) (vi) So the total flux is: ∙ ∙ ∙ ∙ ∙ 2 ∙ 2 1 0 0 ∙ 1 3 1 3 4 3 1 3 102 29
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Chapter One: Vector Analysis The use of vectors and vector analysis ...

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