Fantastic, I thought this thread was dying and then you guys came
along and resurrected it with some incredible insights.
Okay, can you please provide some details on how you obtained your
analytic result?
I think this is how one could proceed, but please correct me: We can
obtain E-vector as 1/4*pi multiplied by a "Helmholtz" (in this case a
"Biot-Savart") type integral of R-vector cross-producted with (c
k-hat) divided by the cube of the magnitude of R-vector. Here
R-vector is defined as the difference between the field position
(r-vector) and the source position (r'-vector), and the integral is a
volume integral over all source elements. Also c is the (constant)
value of dB/dt where k-hat is the unit vector along the z-axis.
Cylindrical coordinates are used, with axes aligned along the
symmetry axes of the square solenoid.
Am I on the right track?
I checked the above procedure for a circular solenoid and it gives
the familiar solution.
I also noticed (yes, I'm a bit slow compared to you guys) that if I
take the curl of the familiar solution (namely r*c/2 inside and
R^2*c/2r outside, both in the azimuthal direction) that I correctly
get c inside and zero outside. (That would make a good homework
problem.) Great, I assume that I could similarly take the curl of
your solution for the square solenoid and get exactly the same
answers.
David, could I STRONGLY urge you to write up your solution and send
it to AJP? I'm confident that John M would agree with me that this is
a very interesting and instructive result that MANY people will be
interested in.
Much thanks also to Bob S for the fantastic MathCad rendering and
Viewer program. It really helped to see the field vectors.
*This* is the kind of thread that makes PHYS-L so great. I wish
sometimes we had more such threads.... -Carl
--
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/