## 2011-04-15

### Wireless Electricity: I Could Have Thought of That

A couple days ago, in my Physics II - Electricity and Magnetism class, our professor was teaching us about mutual inductance, and he was telling us how it never seemed very interesting or useful until it became very important in his own research. He, another professor who was a recitation leader for my physics class last semester, and a few other people created a company called WiTricity which sells equipment for wireless power transmission through magnetic fields, which is sort of like the magnetic counterpart to the Tesla coil, which transmits electrical power without wires through electric fields; the latter is quite dangerous, though, whereas the former is not known to have any ill effects on human health. So how does it work?

Well, our professor had mentioned his work on it a few times in the semester prior to that day, so I figured it was something really complicated. As it turns out, it's just a simple pair of RLC-circuits. One circuit must have an alternating driving voltage, an inductor, and other circuit elements. The other circuit must have an inductor parallel to the first inductor as well as other circuit elements. Basically, the first inductor creates a magnetic field when the driving voltage puts a current through it. The changing magnetic field arising from the current in the first inductor interacts with the second inductor to produce a current in that second inductor. As the driving voltage alternates, it has a certain frequency of alternation. The quality factor of the second inductor is the product of that frequency of alternation (because that frequency is retained in the induced current in the second circuit) and the energy stored in the second inductor divided by the power dissipated in resistors connected to the second inductor (i.e. electronic devices). Furthermore, the mutual inductance of the two circuits, as the two inductors are parallel, is the ratio of the induced electromotive force in the second circuit to the time rate of change of current (resulting from the alternating voltage) in the first circuit. As long as the mutual inductance and quality factor are high and the frequency of change in the current is close to that of the frequency of the driving voltage, which is resonance, it is possible to induce large currents efficiently in the second circuit even if the second circuit is physically relatively far away from the first circuit. Hence, wireless electricity!

I remember reading a while ago that Nikola Tesla also sometimes successfully managed to transmit electrical power wirelessly, and at that time I also thought it must be something really complicated. So I find it funny that it turns out that this is all just based on principles of classical electromagnetism set down in the late 19th century. I guess the reason why no one tried further experiments on it until my professors did a couple years ago is because (a) the equipment wasn't good enough and (b) everyone assumed that this sort of resonant induction wouldn't work for distances comparable to the dimensions of a room and so no one bothered trying to test that. I wonder why that is.

#### 2 comments:

1. more cool is near-field evanescent coupling of coupling of coils. madd cool science. i can send u the paper if you want, but im certain you have access to the paper at school as well (it was done by a founder of Witricity ;)).

2. @somethingquarky: I'd love to see the paper, but if you don't have the link, could you tell me which founder of WiTricity wrote it? Also, here's a fun fact — WiTricity was originally set to be called WiPo, which got changed to WiPoo, which got changed to WiPow, before settling as WiTricity. Thanks for the comment!