why potential energy is considered for the entire system, rather than assigning it to any specific particle ?
Answers
Contrary to most introductory and intermediate textbooks, a single, non-interacting particle cannot possess potential energy. Potential energy is a property of a system of interacting particles and/or fields. A minimum of two entities is required. It is probably more useful to think of potential energy as interaction energy.
The concept of potential energy (or interaction energy) follows nicely from the concept of system. Suppose you have several interacting particles and/or fields (protons in an electric field for example) in your system. Further suppose there are other charged particles outside your system in the surroundings. The system's potential energy is merely a way of accounting for the mutual pairwise interactions within the system. More precisely, the change in the system's potential energy is the opposite of the work done by these internal interactions. See chapter 6 of Matter & Interactions by Chabay and Sherwood (Third edition, Wiley, 2011)