[BUG] curl question

[Tevian Dray]

This is arguably the single most important example of the curl, as it
represents the magnetic field of a current-carrying wire (as in the
lab).  Yes, curl(F)=0 by computation, but only where defined!  The
vector field is only defined away from the origin, so it only makes
sense to compute the curl away from the origin, where it indeed vanishes.

To calculate the curl AT the origin requires care, since F is not
differentiable there, so plugging into the formula doesn't make sense.
But the paddle-wheel argument still works!  The circulation of F around
any closed loop around the origin is clearly nonzero, so the paddle
wheel will turn counterclockwise.  The curl is the limit of the
circulation per unit area for small loops; one can show that this limit
exists, but is a Dirac delta "function" (really a distribution).  In
informal language, the curl is zero away from the origin, but infinite
at the origin.

Good question; hope that helps.

Tevian