Interesting.
The man has slightly different take on the reasoning behind skin depth than the one I've been using for decades; however, most of what I've been doing in that regard has to do with radiation shielding and high frequency (100's of MHz) signals and up. In fact, one year, after getting my Master's degree, I was sort of casually waiting around and doing job interviews while the SO finished up
her degree. Three or so profs knew about that situation, cornered me in my office one day out of the blue, and said, "How'd you like to teach a course in Microwaves this summer, for those looking to pick up three credits? We'll even pay you!"
Next thing you know I'm up on a podium in front of 150 undergraduates, wearing this nifty tee shirt I had found in Alexandria, VA, that had a large Smith Chart printed on it. We all made it through in one piece. Albeit, that was some 36 years ago, but, fun.
Thing is: When one is playing with electricity, there's this duality: Current moving through a wire
forces a magnetic field circling the wire and, if one has a magnetic field circling a wire, that magnetic field
forces electrons to flow within the wire. Two faces of the same coin, actually.
If the magnetic field circling the wire is a constant, then there's a constant current in the wire. Interestingly, at DC, this current is everywhere through the conductor. Now, think about resistance: A piece of copper has a resistivity (so do all metals, there's charts). To get the DC resistance of a wire, one takes the cross-sectional area, divides it into the resistivity, then multiplies
that by the length of said wire. (R = (resistivity/cross-sectional-area)*length) And that's the DC resistance, measurable with ye random ohmmeter.
With AC magnetic fields, things are different. As the energy flows down the wire, the electrons in the wire accelerate, moving towards the positive E field and away from the negative E field; as they do
that, they create an electromagnetic field going the other way. (Think, and I am not joking here, about mirrors.) As a result, if one had perfectly flowing electrons, the electromagnetic field impinging upon the wire would be cancelled by the fields generated by these electrons (weird, but true) - and there'd be current at the surface of the conductor, and none inside, since the EMF (including the magnetic field) would be
cancelled inside. No magnetic field: No electron movement
. Whee.
However, those electrons
aren't free-flowing: Yeah, it's kinda like a gas of electrons in there (that's a defining bit about metals, they
have an electron gas), but as the electrons go flying along, they bump into atoms and get slowed down (Hi, resistance!), making the atoms jostle around (hi, heat!). Since the electrons
didn't accelerate all the way up, the generated counter-EMF doesn't completely cancel the incident EMF.. and the EMF goes farther in, making the next bunch of electrons accelerate (but, again, not all the way up) doing some more cancelling of the incident EMF, and so on. The EMF as one goes into the conductor (with an AC EMF) exponentially decays as one goes in; when the EMF is down by 1/e, that's the skin depth. Go in, say, 5 skin depths, and the current in the conductor is effectively zero.
So, say one is playing with bus bars at 60 Hz. Over at the Power Company, the square bus bars tend to be hollow, since little current flows in the center. Just checking:
skin_depth = sqrt(2*resistivity/(2*pi*frequency*mu)) which, for copper at 60 Hz gives us
sqrt(2*1.68e-8/(2*3.14159*60*4*3.14159e-7*1.0)) = 16.84mm = 0.663".
Since were talking exponential decay, here, 5 times the skin depth results in a current of zero; that's about 3.3 inches. So, if one has a bus bar that's one foot square, then one is going to save a considerable amount of money on copper by making the bus bar hollow with the sides and tops 3.3" thick.
But, notice that in that stupid equation above (and, yeah, that's the simplified one) there's a "sqrt(1/frequency" in there; meaning that as one goes up in frequency, the thickness of copper that's
actually carrying current is getting thinner and thinner. At, say, 10 MHz, that skin depth gets to be 20 um (that's micrometers). Remember what I said about resistance? It's the
cross-sectional area of the conductor. The smaller that is, the bigger the resistance of an a wire; and, if all the current is restricted to the surface of a wire and 5 skin depths deep, that means that the resistance goes
up, the wire gets hotter, and More Losses.
This is why, when one is looking at, say, ham radio transmitters running at 20 MHz or so, big inductors tend to be silver plated, because the current is in the surface of the conductor, silver's the best conductor, and that's a good way to minimize losses.
As one gets into the GHz, the losses on (say) coaxial cable get Really High on that center conductor, to the point where, say, MW-scale RADAR transmitters would loose all the power on the way from the transmitter to the antenna. Hence, waveguides, where we dispense with the center conductor and bounce electromagnetic waves down the interior of hollow,
silver plated (yeah, we got currents there, too, but we spread 'em out) rectangular shaped bars of metal.
Now, back to motors. The point to be made here, and in the video, is that if one is running at, say, 200 kHz or so (I'm guessing that as the switching frequency of the electronics driving the motors), the majority of the current is traveling on the
surface of the wires. Not
in the wires. So, having more surface area
reduces the overall resistance. So, with Teslas old-timey many many wires in each slot, that's a lot of wires: and the amount of surface area in all those wires is a heck of a lot more than, say, three wires in each slot or something, and that reduces the AC
losses in the wire. As compared to the DC losses.
In fact, now that I think about it, he spent a little too much time talking about AC vs DC resistance; it's the AC vs DC
losses that are the point. Losses tend to go as A*A*R; and if the value of R is less, there's less heating in the wires, less energy going to heating up the motor, and more available to move the car forward.
I'm not a motor guy (as if you all couldn't tell), but the story hangs together a bit. Fun.