The Christmas break has finally given me the time to sit down and
carefully write up the solution (including graphs) of the problem
(discussed on this list in November) of finding the induced electric
field for a square solenoid when the current increases at a constant
rate:
There's nothing new in this - it's Bowman's solution plus Sciamanda
and Mallinckrodt's plots. But I find it satisfying to dot my i's and
cross my t's by writing up summaries like this. Maybe someone else
will find it useful. I note the following interesting features of
this problem:
(1) It's the first problem I can remember doing that *required* me to
use the Helmholtz theorem.
(2) It has some very nice integrals to compute. In particular look at
the integration by parts to do the integral given in Eq. (13).
(3) Contour lines and field lines look quite different. I bet most
students would assume contour lines and field lines should look the
same. Throw the plots in this paper at them to chew on.
(4) One could easily be fooled by Eq. (1) into thinking that the
field lines inside a square region should look identical to those
inside a circular region. That equation hides the thorny problem of
the *shape* of the edges of the region. On the other hand, the field
lines are only *slightly* noncircular, so it's not like that guess is
way off base.
Corrections to this summary paper are welcome on or off list. -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/