Thoughts on Zapper design - 1
The item I see repeated frequently regarding frequency is that a lower frequency "penetrates" deeper due to "skin effect".
Skin effect is pretty simple. Since most wire is round, a section of wire conducting electric current basically is a solid cylinder full of copper atoms, each with mobile electrons. At DC (direct current, 0 Hz) the electrons are evenly distributed throughout the cylinder, moseying along from the negative battery terminal to the positive. Switching to an AC power source (sine wave, square wave, whatever), as the frequency increases the electrons and photons rattle back and forth in and around a wire faster and faster, and a funny thing happens. The mobile electrons start to crowd outward toward the surface ("skin") of the wire. So now the part of the copper cylinder toward the center has fewer mobile electrons, and the part toward the surface has more. The higher the frequency, the more outward crowding. At very high frequencies, the wire might as well be a hollow cylinder because there is practically zero mobility down the center. This is where the idea that high frequencies don't "penetrate" comes from. Yes, as the frequency increases the conducting part of the wire (the skin "depth") decreases. But applying that to Zapper operation is apples and oranges.
There are three problems with this interpretation of skin effect. First is that the effect is being misapplied. Remember, the wire has the same number of copper atoms and electrons no mattter what the frequency. They're already in there. High frequency current doesn't penetrate into a wire, it crowds toward the outside **from the inside**. With regards to Zappers, however, penetration should be viewed as the penetration of an electromagnetic field through other stuff. For example, think of home cordless phones. As the frequency of cordless phones has increased through the decades (27MHz, 47MHz, 900MHz, 2.4GHz, 5.6GHz) the range and clarity of the radio link also has increased, even though the transmitted power has either remained the same or *decreased*. Anyone who has used police or construction site walkie talkies knows that UHF radios "penetrate" through walls far better than VHF radios. Same thing: higher frequency = better penetration. This is because the total energy in the wave is proportional to frequency. As frequency goes up, the energy in the wave goes up.
Second problem, the conductor. The skin depth - the thickness of the outer, conducting part of the wire - can be calculated very easily if you know the electromagnetic properties of the conductor. I've done some digging on this, and I don't think the human body is made of solid copper. In fact, from a conductor point of view, the body more closely resembles bundles of smaller "wires" - the vascular and lymph systems. The real result of skin effect is that large wires behave as if they were small wires. If you are trying to conduct a large amoiunt of high-frequency current, the best way is to use bundles of smaller wires rather than one large one. You can move more current with less copper if you do the math. And what are thousands of arteries, veins, and capillaries if not bundles of small conductors? So even if skin effect applies to the body, the body counters it naturally by its construction.
Third problem, the depth. Even if the skin effect actually applied to the situation, and even if the body didn't naturally counteract it, the actual "depth" is trivially small. Nowhere have I been able to find the relative permeability of the human body, but for most non-ferrous conductors it is close to 1.0. At 33KHz, the original Zapper frequency, the skin depth is 14 thousandths of an inch.
At 2.5KHz, a common lower Zapper frequency, it increases to a whopping, enourmous, gigantic 50 thousandths of an inch
- still **less** than one-sixteeth of an inch.
In an average adult, the distance from the shoulders to the lower organs is over a foot. I don't think that extra .038" is going to matter.
There may be a real benefit to zapping with a lower fundamental frequency, but not because of the skin effect.