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
sin
4π
They don’t agree!!!!! !!
Problem:
Compute
the divergence of the function:
cos sin
sin cos
Check the
divergencee theorem for this function, using as
your volume the inverted
hemispherical bowl of radius , resting on the plane
and centered at the origin.
Divergence theorem state:
∙ V ∙
1 ∂
∙V
∂r 1 ∂
sin ∂θ sin 1 ∂
sin ∂φ
1 ∂
1 ∂
∂r cos sin ∂θ si
1 ∂
in sin
sin ∂φ sin cos
1 1
1
3 cos 2 sincos
sin sin sin sin
3 cos 2 cos sin
5 cossin
∙ 5 cos sin sin
/
5 cos sin sin
/
3 5 coscos 2 0 sin