散度的定义（B022）

问题

已知 $\boldsymbol{A}(x, y, z)$ $=$ $P(x, y, z)$ $\boldsymbol{i}$ $+$ $Q(x, y, z)$ $\boldsymbol{j}$ $+$ $R(x, y, z)$ $\boldsymbol{k}$, 则，$\boldsymbol{A}$ 在点 $(x, y, z)$ 处的散度 $\operatorname{div} \boldsymbol{A}$ $=$ $?$

选项

[A].   $\operatorname{div} \boldsymbol{A}$ $=$ $\frac{\partial P}{\partial x}$ $\times$ $\frac{\partial Q}{\partial y}$ $\times$ $\frac{\partial R}{\partial z}$

[B].   $\operatorname{div} \boldsymbol{A}$ $=$ $\frac{\partial P}{\partial x}$ $-$ $\frac{\partial Q}{\partial y}$ $-$ $\frac{\partial R}{\partial z}$

[C].   $\operatorname{div} \boldsymbol{A}$ $=$ $\frac{\partial P}{\partial x}$ $+$ $\frac{\partial Q}{\partial y}$ $+$ $\frac{\partial R}{\partial z}$

[D].   $\operatorname{div} \boldsymbol{A}$ $=$ $\frac{\partial x}{\partial P}$ $+$ $\frac{\partial y}{\partial Q}$ $+$ $\frac{\partial z}{\partial R}$

   答 案   

$\operatorname{div} \boldsymbol{A}$ $=$ $\frac{\partial P}{\partial x}$ $+$ $\frac{\partial Q}{\partial y}$ $+$ $\frac{\partial R}{\partial z}$