I wasn't playing close enough attention as this thread was evolving,
but I just took the time to read from the the archives and I am
confused and unsettled about what I see, especially with regard to
Carl's discussion of the figures at
I completely agree with Carl's expressed concerns. Subject only to
what seems to me the completely uncontroversial interpretation that
we are asking about the E field that is induced by the specified time
changing B field and are disregarding any other preexisting or
background fields, it is clearly (is it not?) the case that the lines
of the induced E-field are closed and exhibit considerable symmetry,
but are non-circular. Indeed, I would expect them to approach
circularity as r -> 0 and as r -> infinity, but to be somewhat
"squarish" for radii near L/2.
In any event the calculation of E shown in Note 2 is clearly wrong
because it assumes in step 2 a symmetry that does not exist. The same
objection applies to Note 3.
It may very well be that I am simply misunderstanding John Denker's
points, but I keep reading them as suggesting that the lines will
indeed be circular and that there is nothing fundamentally wrong with
the derivations that Carl questioned.