对球面波\(F=\vec{r}/r’\)，\(r=(x-vt,y,z), r’=(\gamma(x-vt),y,z)\)，
\( F=\frac{(x-vt,y,z)}{\sqrt{(\gamma(x-vt))^2+y^2+z^2}}\)
由于\(x\)方向多了个\(\gamma\)，
求旋度，
\(\nabla \times \mathbf{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right)\mathbf{i} - \left( \frac{\partial F_z}{\partial x} - \frac{\partial F_x}{\partial z} \right)\mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right)\mathbf{k}\)
y分量：
\(\frac{\partial F_z}{\partial x} - \frac{\partial F_x}{\partial z} = -\frac{\gamma^2 z(x-vt)}{r’^3} + \frac{z(x-vt)}{r’^3} = \frac{z(x-vt)(1-\gamma^2)}{r’^3}\)
产生了\(1-\gamma^2\)的差值，于是产生了y方向的偏转，同理，也产生了z方向的偏转，最终产生了旋度。
最终结果：
\(\nabla \times \left( \frac{\vec{r}}{r’} \right) = \frac{\gamma^2 v^2}{c^2} \left( 0, \frac{z(x-vt)}{r’^3}, -\frac{y(x-vt)}{r’^3} \right) \)
对t求导：
\(\mathbf{F} = \frac{\vec{r}}{r’} = \left( \frac{x-vt}{r’}, \frac{y}{r’}, \frac{z}{r’} \right)\)
z分量：
\(\frac{\partial F_z}{\partial t} = z \cdot \frac{\partial}{\partial t} \left( r’^{-1} \right) = -z \cdot \frac{ \frac{\partial r’}{\partial t} }{ r’^2 } = -z \cdot \frac{ -\gamma^2 v (x-vt)/r’ }{ r’^2 } = \frac{ \gamma^2 v z (x-vt) }{ r’^3 }\)
得：
\(\frac{\partial \mathbf{F}}{\partial t} = \frac{v}{r’^3} \left( -(y^2 + z^2), \gamma^2 y (x-vt), \gamma^2 z (x-vt) \right) \)
于是可得：
\(\frac{v}{c^2} \left( \frac{\partial \mathbf{F}}{\partial t} \right)_y = (\nabla \times \mathbf{F})_z\)
\(\frac{v}{c^2} \left( \frac{\partial \mathbf{F}}{\partial t} \right)_z = -(\nabla \times \mathbf{F})_y\)
同时：
\((\nabla \times F)_y =(1-\gamma^2)\frac{z(x-vt)}{r’^3}\)
和：
\(\frac{\partial F_z}{\partial t} = \frac{ \gamma^2 v z (x-vt) }{ r’^3 }\)
也预示着等式：
\(\frac{v}{c^2} \left( \frac{\partial \mathbf{F}}{\partial t} \right)_y = (\nabla \times \mathbf{F})_z\)
\( \frac{v}{c^2}(-v \gamma^2 E_0^2)= (1 -\gamma) E_0^2 \),
如果 \( E_0^2 = \frac{z(x-vt)}{r’^3}\)
则：\( (\gamma E_0)^2 =\frac{v^2}{c^2} (\gamma E_0)^2 + E_0^2 \),
即：
\( E^2 =(cB)^2 + E_0^2 \),
说明旋度是\(E^2-E_0^2\)产生的，也是\(E\)的时间变化产生的
如果\( E_0 = \frac{z(x-vt)}{r’^3}\)
则：\( \gamma^2 E_0 =\frac{v^2}{c^2} \gamma^2 E_0 + E_0 \),
即：
\(\gamma E =\frac{v^2}{c^2}\gamma E + E_0 \), \(E =\frac{v^2}{c^2} E + E_0/\gamma \)
由：
\(\frac{\partial F_z}{\partial x} = -\frac{\gamma^2 z (x - vt)}{r’^3}, \quad \frac{\partial F_z}{\partial t} = \frac{\gamma^2 v z (x - vt)}{r’^3}\)
可知：
\(\frac{\partial F_z}{\partial x} = v\frac{\partial F_z}{\partial t}\)
对任意行波函数\(f(x,t)=g(x-vt)\)，都有：
\(\frac{\partial f}{\partial t} = -v \frac{\partial f}{\partial x}\)