# del operator, divergence , and the curl

In physics the del operator is fundamental.The basic laws of Electromagnetism are defined using it.I wanted to know the actual significance of the curl ( $\nabla \times$)and divergence.I also intended this post to be a starter for a discussion about mathematical fields,their difference and applications(in physics or other subjects).
One reason why $\nabla$ is so important is that it is invariant under rigid motions: rotating or translating the coordinate system does not change the form of $\nabla$. Roughly speaking, the "divergence", $\nabla\cdot \vec{v}$, measures how much a vector field "spreads out" (diverges) while the "curl", $\nabla\times\vec{v}$ measure its tendency to rotate- hence the names "divergence" and "curl".