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Re: [Phys-l] induced electric field



John Denker wrote:
/snip/
I saw in my
mind's eye this picture of the E field inside
a betatron:
http://www.av8n.com/physics/non-grady.htm#fig-betatron
I am quite uncertain how a conceptual Betatron entered the discussion.
By its nature, its vacuum raceway has a non uniform magnetic field in space to handle the relativistic mass or momentum effects etc (by varying with radial distance from the center, in fact, just as John's pictorial shows: given a big whorl equals a small magnitude and the opposite...).
Furthermore, a Betatron has a magnetic field that varies cyclically in time.

In contrast, what we seem to be discussing is a magnetic field uniform in space, and increasing in time. An electron enclosed in such a space will curve if it moves: and move equally at any part of that uniform field, square, circular or star-shaped....


I suppose I should add that if I take a circle specified by a one dimensional curved line, then it has a specific direction; but only if I simply take the infinitesimal limit of a part of its periphery.
This too seems an unhelpful observation in this context.

Brian W