Looking at the 2nd panel (Note 2), I venture to say that circled step
2 does not actually give E because I think E isn't constant along a
circle inside a square B-field region. However I could replace E in
that step by E-tan-avg (the average value of the component of the
E-field tangential - or azimuthal - along the circular path).
I think I can also say that by symmetry E must be purely tangential
at certain points along the circle, namely at the 4 points where it
intersects the straight diagonal lines and at the 4 points where it
intersects similar horizontal and vertical lines, ie. at the 8
compass points N, NW, W, etc.
So all this is a start. Can anyone go on and say more so we can make
more progress? -Carl
ps: The question of how to produce a uniform B inside a square region
(and zero outside) is a different issue, and also not particularly
obvious to me. Just winding a solenoid around a square form
presumably won't do the trick. (Because we then have a similar
problem to the lack of circular symmetry for Faraday's law - except
now for Ampere's law.) I could use a C-shaped magnet with square
cross-section and a tiny gap and ignore (probably to my peril) the
fringing field.
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363 mailto:mungan@usna.eduhttp://usna.edu/Users/physics/mungan/