The conversation between Hal Davis and Robbie Rhodes regarding magnet
force is interesting to me, too.  Jeff Borinsky and I discussed it
privately, and we had a very interesting and enjoyable discussion, too.
A savvy guy.

I have to take Hal's side on the voltage issue, since I know that
magnets and solenoids, while being basically "power driven," are a bit
like motors or any inductor, in which low voltage and high current incur
a bit more losses than do higher voltage/lower current.

It seems to me that the ratio of the fixed resistance of the windings to
VA (apparent power) is better when the voltage is higher.  Inductance is
indirectly proportional to the current, not the voltage, but the back emf
(force) of the circuit is the mirror of the voltage in the circuit, given
the same current.  So it seems to me that it would be easier to minimize
the heating losses by increasing (somewhat) the voltage.

I'm talking about optimization here, because ultimately, you will expend
approximately the same amount of energy in heat, but the action of the
solenoid would be initially stronger because of the permeability curve
of the iron, and where its saturation point is located.  It's really an
integral equation as I recall, but I have been out of this field for so
long, someone may want to correct me on this.

(Also, I have always wondered how engineers and scientists contained
themselves, never being able to communicate formulae on their own web?
It's driving me nuts, too, and I don't even want to be known as one of
"those!")

If I had the problem to solve on the bench again, I'd just take some
simple force measurements and leave the doctors of mathematics alone to
conjugate their navels.  I've already been through that, and I don't
intend to do it all over again.  Now that we're back to writing letters
to each other, though, I imagine I'm going to have to get out my text
books for such rash, un-intellectual statements.  Right?  Wrong!  Let me
just quote this famous line at the outset, "I know nothing!"  (Quoted
from my hero-- Sargent Schultz).

Craig Brougher