球面座標系
d i v A = ∇ ⋅ A = e r ⋅ ∂ A ∂ r + e θ r ⋅ ∂ A ∂ θ + e φ r sin  θ ⋅ ∂ A ∂ φ = ( ∂ A r ∂ r + 2 r A r ) + 1 r ( ∂ A θ ∂ θ + A θ cot  θ ) + 1 r sin  θ ∂ A φ ∂ φ = 1 r 2 ∂ ( r 2 A r ) ∂ r + 1 r sin  θ ∂ ( A θ sin  θ ) ∂ θ + 1 r sin  θ ∂ A φ ∂ φ {\displaystyle {\begin{aligned}\mathrm {div} \,{\boldsymbol {A}}&=\nabla \cdot {\boldsymbol {A}}={\boldsymbol {e}}_{r}\cdot {\frac {\partial {\boldsymbol {A}}}{\partial r}}+{\frac {{\boldsymbol {e}}_{\theta }}{r}}\cdot {\frac {\partial {\boldsymbol {A}}}{\partial \theta }}+{\frac {{\boldsymbol {e}}_{\phi }}{r\sin \theta }}\cdot {\frac {\partial {\boldsymbol {A}}}{\partial \phi }}\\&=\left({\frac {\partial A_{r}}{\partial r}}+{\frac {2}{r}}A_{r}\right)+{\frac {1}{r}}\left({\frac {\partial A_{\theta }}{\partial \theta }}+A_{\theta }\cot \theta \right)+{\frac {1}{r\sin \theta }}{\frac {\partial A_{\phi }}{\partial \phi }}\\&={\frac {1}{r^{2}}}{\frac {\partial (r^{2}A_{r})}{\partial r}}+{\frac {1}{r\sin \theta }}{\frac {\partial (A_{\theta }\sin \theta )}{\partial \theta }}+{\frac {1}{r\sin \theta }}{\frac {\partial A_{\phi }}{\partial \phi }}\\\end{aligned}}}
と書ける。