⁷⁵The term $curl$ is mostly used within the US, instead of rotation. The $rot$ -operation gives how and how much a vector field rotates in space; the $div$ -operation takes the derivative of a vector field. In mathematical form: $rot (F) \equiv \nabla \times F$ , $div (F) \equiv \nabla \cdot F$ and in 3-dimensions with $F = [F_{x} F_{y} F_{z}]$ :

\nabla \times F = | \begin{matrix} e_{x} e_{y} e_{z} \\ \frac{\partial}{∂x} \frac{\partial}{∂y} \frac{\partial}{∂z} \end{matrix} |

\nabla \cdot F = \frac{\partial F_{x}}{∂x} + \frac{\partial F_{y}}{∂y} + \frac{\partial F_{z}}{∂z}

where

e_{x}

e_{y}

e_{z}

are unit vectors in x, y and z direction. Tricky, indeed, which is why I explain as less as possible in this reader.

The “ $\times$ ”-operator means the vector product, giving a vector which is perpendicular to the original two vectors: something with the right-hand rule. To transmit energy with an EM-field, we need a 3-dimensional world. Therefore, a 2-dimensional world would be completely dark, since light is a special form of an EM-wave.