Do we know why the field produced by charge extends to infinity? Do we have any model to show why charge field or magnetic field extends till infinity. 
Edit: I agree that according  to coulombs law $1/r^2$ cannot be 0 but do we know why this happens.I think I am looking for a physical model.
(correct me if i am wrong)
 A: Electric field extends to infinity in the sense that no limit after which the field would vanish was ever found. It is natural assumption that simplifies things. Coulomb's law is consistent with this assumption, but there is no model that would explain Coulomb's law from anything simpler.
A: Actually we have models explaining this. The particles that mediates electromagnetic field are massless, so the range of the force predicted by the model is infinite. On the contrary, for massive mediators (see for instance Yukawa force), the range is finite.
Notice that real experimental setups have finite precision, so beyond some limit it's pointless to make measurements (not to mention noise, quantum uncertainty, and so on).
A: I'm not a physicist and came to the problem of infinity of the electric field by working about Complex one-dimensional structures in space. In this work I recognized that to build-up dipole fields it needs two different quanta at least and only. Such structures could follow the 1/r²-law, BUT related to the discrete structure the field has a finite range. Why this was not observed until now? First at all the quanta have to be in a range of energy much smaller the photons. Second, the need in the description of quantized force dipole fields seems not to exist until now. But your question and the really good comments to your question encourages me to answer your question. 
The consequences of the postulate about quantized force dipole fields are strange. Field lines of dipole fields have a reality. Magnetic field, electric field and electromagnetic radiation are built from the same quanta. You name it after you read my elaboration about  Complex one-dimensional structures in space. The original paper is in German: Komplexe eindimensionale Strukturen des Raumes. Quantenstruktur der Photonen.
The consequences are enormous and the teachers in this forum perhaps will not be prepared to think about this, they want to defend the mainstream. The scientists in this forum perhaps are busy with their own problems and solutions, but since they are here perhaps will pay attention and will attach criticism.
