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
0
0
0 1 0
√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(25):
Show that if the scalar function , is harmonic at point √3, ,0 .
∂
r sinθ ∂θ
H 1 ∂
r ∂r r sin θ e 1
H 1 ∂ ∂H
r r
∂r ∂r 1
∂H
sinθ
∂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 θ2sinθ 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
Home Work:
Q 1 / Prove that: ( V A ) V
A AV
, where V is a scalar field and A is a vector field ?
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