Original poster: Gregory Morris <gbmorris@xxxxxxxxx>Yes, as I learned in my Electricity and Magnetism course last year, the electrons are individually moving extremely fast, but in rather haphazard directions; their actual displacement per time in a conductor is more on the order of 10^-4 m/s. But nonetheless I can't help wondering if his proposal has some merit...
Consider:Current, I, is charge per unit time, specifically 1 Coulomb per second, or about 6.25*10^18 electrons per second, having a combined mass of around 5.7*10^-12 kg. Let's call our mass per unit time k = I/qe*me, where qe and me are the charge and mass of an electron respectively. Moment of inertia, which we will call M, of a point mass is equal to mr^2, where m is mass and r is path radius. So for our purposes we have mass per unit time, k, and the total mass can be found by multiplying by the time each charge spends in the conductor, which is equal to l/veff where l is total length of the conductor and veff is the effective velocity of electrons (around 10^-4 as stated above.) Conductor length, l, can be found from the radius of the inductor and the number of turns, N, it has, that is l = 2pi*r*N. So now we have M = k*(2pi*r*N)*r^2/veff or M = 2pi*k*N*r^3/veff. The energy stored in a rotating mass with a moment of inertia is E = 1/2 M omega^2, where omega is angular speed and equals v/r, so E = 1/2M(v/r)^2 = 1/2 (2pi*k*N*r^3/veff)(veff/r)^2 = pi*I*me*N*r*veff/qe, and finally if we substitute the values we have, me, qe, pi, and our veff which we will assume to be 10^-4, the energy stored in an inductor is E = 1.8*10^-15 * I*N*r, if all my arithmetic makes sense.
Similarly energy stored in the magnetic field of an inductor is E = 1/2 L*I^2, where L is inductance, and I is current. Inductance, can be calculated by the formula L = uo*ur*N^2*A/x, where uo is the permeability of free space (4pi*10^7 H/m), ur is the relative permeability of the core, which for an air core is about 1, A is area of the coil, and x is length of the solenoid. A = pi*r^2, so we have L = uo*N^2*(pi*r^2)/x and E = 1/2 uo*N^2*pi*r^2*I^2/x or E = 2.0*10^8*(I*N*r)^2/x.
Now these results are of different forms and wildly different magnitudes, which might cause some of you to immediately say this is an elegant proof of why the two principles are irreconcilable, I would disagree and say it isn't especially elegant. But either way it is clear that by taking a more reasonable electron velocity into account, moment of inertia and inductance are not the same phenomenon. They share some common properties (for example the terms I, N, and r appeared in both results, if in different powers), and I would be interested to see what would result from assuming a relativistic electron velocity and maybe by doing that, managing to take the length, x, of the solenoid into account in the inertial problem. But not by me, or at the very least not tonight, as it is late and I am going to bed.
Goodnight, Greg Tesla list wrote:
Original poster: "Gerry Reynolds" <gerryreynolds@xxxxxxxxxxxxx> Hi Jared,I'm wondering if there may be a misconception about how electricity travels in the wire. Given a segment of wire that is part of a complete circuit and suddenly energized at one end so that an electron enters that end of the wire, a certain time later an electron will exit the other end of the wire. The propagation time from one end to the other end is indead close to the speed of light (0.95C for copper, I think). However, the electron that exits is not the same electron that entered the wire. If one were to somehow tag the entering electrons, one would find that their propagation is much much slower than C. The thing that is propagating thru the wire at 0.95C is not the electrons but is the electrostatic force caused by the electrons entering the wire. At least this is what I believe I was taught. Someone more knowledgable can correct or fill in the details.Gerry R.Original poster: "Jared Dwarshuis" <jdwarshuis@xxxxxxxxx>Charge is traveling in a circular path at the fixed velocity of C. The charge has a relativistic mass. As we increase the radius of our inductor for a given wire length, we increase the moment of inertia. As the system inertia increases so does the inductance.Sincerely: Jared Dwarshuis, Larry Morris