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

Electromagnetic Theorem
(Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department
b) Test the divergence theorem for this function, using the quarter‐cylinder (radius 2, height
5) shown in Fig.
c) Find the curl of V.
a))
∙V 1
∙V 1
∂
∂
∂
∂ 1
2
sin φ
1
∂
∂φ ∂ ∂z
∂
sinφcos
∂φ φ ∂ ∂z 3
∙ V V 1
2 2sin φ
1 cos
φsin φ 3
∙V 4 2 sin φ cos φ sin φ3
∙V 7sin φcos φ
b)) Divergence theorem state:
∙V 8
∙ V ∙
∙ 8
Mean while, the surface integral has five parts:
8
/
82
5 40
2
Top: 5 ;
Bottom: 0
V ∙ 3 15
V ∙ 15
15
;
/