If we consider a source, radiating electromagnetic radiation in all directions, intensity falls off as 1/r^2, and thus electric field amplitude falls off as 1/r. But if I consider exactly one wave emanating from the source, there is no way that that one day can lose energy and therefore it's amplitude of electric field has to be a constant. Whats wrong with my analysis
The energy is spread out over a larger surface area as the wave expands. The electric field squared is proportional to the energy density, not the energy. So as the wave expands, the energy per unit area goes down, but the area goes up, in a way that keeps the total energy of the wave fixed.