Reading about impedance has convinced that Larson is wrong about the dimensions of capacitor charge (Q=t/s) and capacitance (C=s).
First up is the common formula f=1/(2pi*sqrt(L*C)). This only works if Capacitance=s3/t
I just spent a couple hours digging through the equations, and I believe you are right. When capacitance and inductance are viewed separately, Larson's values work. But, when you start connecting them together, as in resonant circuits, Larson's units DON'T work--but yours do (at least with Larson's definitions of magnetism, which may or may not be correct at this point).
I did notice there seems to be a mixup between Q (t/s), q (s) and C (s) and C (s3
/t), since they are numerically interchangeable in most cases, having a value of 1 natural unit.
Also, capacitance depends not only on Area over distance, (s2/s=s), but also on the permittivity (s2/t) of the dielectric - again, the Farad is really s3/t.
Rainer was telling me of an experiment an instructor did in school, where they had a large capacitor that could be disassembled. They charged up the capacitor, removed the dielectric, and passed the plates around the room to the students. There was no apparent "charge" on the plates. The plates were returned and the dielectric placed back between them, and the wires shorted--ZAP--huge discharge. This demonstrated that the so-called "charge" is actually contained in the dielectric, not the plates, which means the energy would be proportional to volume
as you indicated, not just the distance.
Rainer and I were discussing the capacitive situation just moments ago, trying to figure out what is being "stored", given your modification. The dimensions of s3
/t can also be interpreted as I x s2
, current times area (current--uncharged electrons--are proportional to the cross-section of the wire). Rainer's argument was that there is no current flow in the capacitor, but if consider the situation, "I" is just s/t... electron (s/1) EXISTING in time region (1/t) as "motion" (s/t)--not necessarily "something moving", so you can think of the current as an "electron distance", since electrons ARE units of space (distance), along with the area, comprising a volume. The temporal component is then a property of the time region, 1/t, giving s3
It also supplies some insight into the nature of capacitance, itself. Unlike what conventional electronics says, what is being stored are uncharged electrons
("holes" or positive charges) in the time
of the dielectric. Remembering the reciprocal relationship between space and time, a decrease in space is tantamount to an increase in time, so the closer the plates are together in space, the further they are in time. But you need something to "pivot" on for that. The spatial displacement of the dielectric is basically increasing the "space" between the plates, and since that "space" is coupled with a time region, that compression results in more time in less space--the pivot point. Also, the space prevents the flow of electrons across the plates, since the relation of space (electron) to space (dielectric) does not constitute motion.
By using Dave's value in the regular equations concerning capacitance and energy, some flipping between Q (t/s) and q (s) is necessary, but they still work.
Fascinating discovery, Dave!!
Every dogma has its day...