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 √9165 √25 5 0 5 90 4 3 53.13 5sin90 cos53.13 5 0 cos90 sin53.13 5cos90 cos53.13 5 0 sin 90 sin 53.13 . 3 0 0.018 Example(7): Determine the flux of through the entire prism shown in Fig. Solution: z c The equation of surface (abc) is: 1 1 ,3 ,6 6 2 6 ⟹ 662 x a b y The equation of line (ab) is: ⟹ 3 3 ⟹ 3 3 To find flux through the entire prism we can use divergence theorem: ∮ . ∙ ∙ 3 . 3 . 3 6 6 2 . 3 63 3 63 3 2 3 3 2 60
Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department . 27 . 27 1 3 1 4 1 5 7.65 Example(8): Show that if the scalar function , is harmonic at point √3, ,0 . Solution: ∂ ∂θ H 1 ∂ r ∂r r sin θ e 1 H 1 ∂ ∂H r r ∂r ∂r 1 r sinθ sinθ ∂H ∂θ 1 ∂ H r sin θ ∂φ ∂ r sinθ ∂θ sinθ2 sin θ cosθ e H sin θ r r e 2r e 2 e r sinθ sin θ 2sinθ cos θ H sin θ r e r2 2 e r 2 cos θ sin θ At point √3, ,0, H0 ⟹ is not harmonic. 1 r sin θ 0 Example (9): Display whether the field vector is solenoid, conservative or none of them? Solution: (1). In order to show that the field is solenoid, it must be satisfy: ∙A 0 ∙A 1 r ∂ ∂r r A 1 rsinθ Therefore the field is not solenoid: ∂ ∂θ sin θ A 1 ∂A rsinθ ∂φ ∙A 1 r ∂ ∂r r 1 r r 3 0 (2). In order to show that the field is conservative, it must be satisfy: A 0 1 1 0 0 1 00 00 00 0 Therefore the field is conservative. 61
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