##### 旋度 - 旋度 - **旋度**是[[向量场]]在某点的向量值, 描述场在该点的局部旋转特性, 其方向表示旋转轴, 满足右手法则, 模长表示旋转强度, 可作为[[向量算子]], 形式上是[[梯度]]与向量场的[[叉积]]. , 若 $\nabla \times \mathbf{F} = 0$, 则向量场是无旋场 - $\mathbf{F}=F_1(x,y,z)\mathbf{i}+F_2(x,y,z)\mathbf{j}+F_3(x,y,z)\mathbf{k}$ - $\displaystyle\text{curl}\ \mathbf{F}=\nabla\times\mathbf{F}=\left(\frac{\partial F_3}{\partial y} - \frac{\partial F_2}{\partial z}\right)\mathbf{i}+\left(\frac{\partial F_1}{\partial z} - \frac{\partial F_3}{\partial x}\right)\mathbf{j}+\left(\frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y}\right)\mathbf{k}$ - $\displaystyle\text{curl}\ \mathbf{F}= \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac {\partial}{\partial z} \\ F_1 & F_2 & F_3 \end{vmatrix}$