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Phaier School
Divergence (発散)
∇
⋅
A
=
∂
A
x
∂
x
+
∂
A
y
∂
y
+
∂
A
z
∂
z
=
1
ρ
∂
(
ρ
A
ρ
)
∂
ρ
+
1
ρ
∂
A
ϕ
∂
ϕ
+
∂
A
z
∂
z
=
1
r
2
∂
(
r
2
A
r
)
∂
r
+
1
r
sin
θ
∂
∂
θ
(
A
θ
sin
θ
)
+
1
r
sin
θ
∂
A
ϕ
∂
ϕ
\begin{aligned} \nabla \cdot \mathbf{A} & = {\partial A_x \over \partial x} + {\partial A_y \over \partial y} + {\partial A_z \over \partial z} \\ & = {1 \over \rho}{\partial \left( \rho A_\rho \right) \over \partial \rho} + {1 \over \rho}{\partial A_\phi \over \partial \phi} + {\partial A_z \over \partial z} \\ & = {1 \over r^2}{\partial \left( r^2 A_r \right) \over \partial r} + {1 \over r\sin\theta}{\partial \over \partial \theta} \left( A_\theta\sin\theta \right) + {1 \over r\sin\theta}{\partial A_\phi \over \partial \phi} \end{aligned}
∇
⋅
A
=
∂
x
∂
A
x
+
∂
y
∂
A
y
+
∂
z
∂
A
z
=
ρ
1
∂
ρ
∂
(
ρ
A
ρ
)
+
ρ
1
∂
ϕ
∂
A
ϕ
+
∂
z
∂
A
z
=
r
2
1
∂
r
∂
(
r
2
A
r
)
+
r
sin
θ
1
∂
θ
∂
(
A
θ
sin
θ
)
+
r
sin
θ
1
∂
ϕ
∂
A
ϕ