2009/8/24 Shachar Shemesh <shac...@shemesh.biz> > Michael Vasiliev wrote: > > The power of the signal is inversely proportional to the square of > distance. > > That is not precisely accurate. > > An undirected point source of EM radiation (or any other type of energy) > transmits energy that expands on a sphere from the point of transmittal. The > surface area of the sphere expands proportionally to R^2. Therefor, the law > of conservation of energy dictates that the energy received over a constant > area receiver (say, a 1 cm^2 energy receiver) will decline proportionally to > the square of the distance from the transmitter. > > As a side note - does that prove that our universe only has three > dimensions? >
It only means that your problem has a symmetry of 3 dimensions. Consider an ideal omnidirectional antenna on the plane - sends an identical signal to the same height, and nothing above and below. Then the energy loss would indeed be 1/R. This only means that the omnidirectional antenna is a problem with 2D symmetry, not that the world has less dimensions. Flatland phylosophy is always clearer. http://en.wikipedia.org/wiki/Flatland > > However, if our transmitter is directional, and you keep the transmitter > beam focused, so that it does not expand, there is no reason for the energy > to almost not discard at all. Of course, the medium through which you > transmit the energy may absorb some of it (assuming it is not a vacuum), and > it may disperse some more of it, but there is no reason to get 1/R^2, or > even 1/R. > In order not to lose energy at all, you will need an ideal wave guide ( http://en.wikipedia.org/wiki/Waveguide). If we stick to the air as our media, then you will need a unidirectional antenna. This is also an idealization, as an antenna which points to one direction, projects energy to the opposite direction as well, and there is also significant power loss to the sides. Orna. > Shachar >
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