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
But, is negative and is positive hence must be between 90 and 180 , so add 180 to
:
33.69 180 146.31
10sin42.03 cos146.31
10cos42.03 cos146.31
10sin146.31
5.57 6.18 5.547
Example(21):
A particular vector field cos sin , is in the cylindrical system. Find the
flux due to this field over a close surface of the cylinder 4 , 01 , verify the
divergence theorem.
Solution:
z
(1)
(3)
(2)
y
Surface (1):
Surface (2):
Surface (3):
∙ cos sin ∙ 0
∙ cos sin ∙ 0
∙ cos sin ∙
cos
4 1cos2
sin 2
32
2 64
The divergence theorem state:
∙ ∙
∙ 1
1
x
1
cos 1
sin 0
70