How to create a vector field whose Curl and Divergence are zero at any point? What is the mathematical procedure to derive a vector field whose curl and divergence are zero at any point at any time?
Edit: Please explain it by solving the differential equations of curl and divergence.

A nice example in physics is the standard expression for a dipole field, either magnetic or electric. With the exception of the origin, where the dipole is located, div and curl are zero, and so must also satisfy the Laplace equation. But, wait! del$^2$$\left(\frac{1}{r}\right)$ is $-4\pi$ (Dirac $\delta(r)$) ...ah grass hopper...
