Is there any frequency at which cars can be charged with using wireless? Surely, wireless transmission can be safely assumed to be a form of energy transfer, and there can be charging of cars without physical electric outlets. Is there a frequency at which cars can be charged? One can see the problem of energy transmission as a form of optimization problem in which the parameter energy (E) is to the transmitted with maximal effect(I could be nebulous here!) Is there such a frequency for wireless car charging?
There is no way one can answer this question without further requirements. In practice, engineering considerations will put wireless charging of vehicles probably somewhere between the 20kHz and 150kHz range (unless the regulator permits a higher frequency). Why 20kHz? Because all wireless charging solutions will involve the generation of some amount of acoustic noise, and it's a good idea to put that noise above the human audible range. Why 150kHz? Because in the US the restrictions on electromagnetic noise are much more lenient below 150kHz than above (there are important wireless services running above 150kHz, and noise sources have to be minimized).
In general, there is a fairly trivial formula for switching power supplies that relates the volume of magnetics and the switching frequency for a power transfer application. The power P is proportional to the product of magnetics volume V and switching frequency f: P=const*V*f. The constant depends on the materials used and the details of the design, but it's pretty similar for most technically viable solutions. So this means, that engineers simply have to pick the power they want to transmit, and that pretty much determines the product of magnetics volume and switching frequency. Switching losses are increasing rapidly above a few hundred kHz, so that, again, pushes converters above 20kHz for the stated reasons, but probably keeps "optimal" designs somewhere below the low MHz range. And, like I said, if you want to make your life easy with the FCC, stay below 150kHz.
It seems there is a Light duty guideline for charging electric vehicles in the wireless medium. There are power, and frequency guidelines that are being set at the present time to charge electric vehicles. The SAE(Society of Automotive Engines) task force has agreed on the frequency of 85kHz, as the frequency standard for charging vehicles. The power requirements are varied, and they have three different power transfer requirements, that of 3.7KW, 7.7 KW, and 22 KW. There is a standard being developed for the proposed wireless energy transfer for cars, at this time.