Amplitude of electromagnetic waves We know that an electromagnetic wave is produced by periodically changing electric field (by an accelerating charged particle). We know that the electric field of a point charge varies inversely with square of distance from the charge. Therefore the amplitude of the electromagnetic wave such as light must go on decreasing and practically vanish on covering a finite distance. But , as we know, it doesn't happen and we see the light waves coming from stars very far away. Then what's happening there? Or am I wrong? Please  explain.
 A: The reason we can see stars from far away is because those stars are unimaginably bright up close. Stars do vary in brightness depending on the star type and distance, and there are certainly stars whose light we cannot see. Read about apparent magnitude and absolute magnitude.
A: 
We know that an electromagnetic wave is produced by periodically changing electric field (by an accelerating charged particle).

Photons are emitted by accelerated charges. The energy of the photons depends on the strength of the acceleration, e.g. small accelerations of electrons lead to infrared radiation and braking radiation Bremsstrahlung to X-rays or gamma radiation.
mostly
The electric field you mentioned is needed, for example, in an antenna rod for the forward and backward acceleration of electrons. As a result, the electrons emit polarized photons and one is able to identify a common oscillating electric and a common oscillating magnetic field from all these photons. Such radiation has the properties of an electromagnetic wave.
The light or electromagnetic radiation from the sun is mostly the result of the chaotic acceleration of charges and the flow of the emitted photons does not have the properties of a wave.

... the amplitude of the electromagnetic wave such as light must go on decreasing and practically vanish on covering a finite distance. But , as we know, it doesn't happen and we see the light waves coming from stars very far away.

The amplitude of EM radiation has to do with the intensity of the light. The intensity of a monochromatic radiation - all photons of the same wavelength - has to do with the number of photons through a given area in a given time.
The potential decrease of intensity is only correct if there is an indistinguishable number of photons. But there are stars so far away that their observation is only possible by collecting single photons. Thus the potential decrease is right only other a long time of observation and the energy packages which arrive the earth are discrete one.
