球坐标变换

单位矢量

关于$\overline{e_{r}} , \overline{e_{\theta }} ,\overline{e_{\varphi }} 和\overline{e_{x}} , \overline{e_{y}} ,\overline{e_{z }}$的转化

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立体角

定义：投影面积与球的半径平方之比
面积微元dA：$dA=rd\theta \cdot rsin\theta d\varphi$

$$d\Omega =\frac{dA}{r^{2} } =sin\theta d\theta d\varphi$$ $$\int _{A} d\Omega =\int_{0}^{2\pi } d\varphi \int_{0}^{\pi } sin\theta d\theta =4\pi$$