Re: [Phys-l] induced electric field

[John Denker <jsd@av8n.com>]

In answer to the question of how I knew what the field
was going to look like, I previously said:

> It is complicated to explain, because there are
> about ten arguments that all lead to the same
> conclusion, and probably all ten of those neurons
> were firing in my brain at the same time.

In addition to the various arguments already 
discussed, here is yet another that leads to
the same conclusion.  I didn't mention it 
previously because it is impossible to explain
without fancy diagrams ... and it takes me a
while to generate the diagrams.

It really helps to keep track of what the flux is
doing _in four dimensions_.

The classic idea of "flux lines" is very useful, 
even though the standard version of the idea has 
a number of limitations and imperfections.

It turns out that if you modify the flux line idea 
a little bit, and extend it to four dimensions, it
becomes tremennnndously powerful and has direct
physical significance.

You can actually make pictures of Maxwell equations.

In particular, you can see that any electromagnetic
field that can be described as having a changing 
magnetic field *must* also be described as having
an electric field.  The four-dimensional geometry
of the situation demands it.

If you want to see how this works, take a look at
  http://www.av8n.com/physics/flux-tubes.htm

This is a brand-new document.  Don't expect a high
degree of polish.  As always, comments and suggestions
are welcome.