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*From*: Carl Mungan <mungan@usna.edu>*Date*: Thu, 7 Jan 2010 17:01:22 -0500

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:

http://usna.edu/Users/physics/mungan/Scholarship/InducedElectricField.pdf

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.edu http://usna.edu/Users/physics/mungan/

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