Superposition Principle for Electric Fields If there is a collection of charges $q_1,q_2,q_3....q_n$, and we want to calculate the total Electric Field due to all these charges at a point $P$ ,then the we sum them all up by the principle of superposition.
$$E_{tot}=E_{1P}+E_{2P}....E_{nP}  $$
Where $E_{nP}$ is the field due to the $n^{th}$ particle at point $P$.
I know that this superposition principle has been proved experimentally, but is there a more deeper reason as to why this happens? Why is the field at a given point independent of the fields due to other charges. I mean it could have also been something like:  $E_{tot}=E_{1P}$ x $E_{2P}$ x .... x $E_{nP}  $. Is there  a particular reason for nature to act this way?  I am sorry if this is a stupid-silly question.
 A: The effect of each charge appears to be completely independent of the effects of other charges.
So those effects get summed.
The effects of different charges sort of cross right over each other without affecting each other. Like ripples on a pond cross each other and continue, each unaffected by the others.
It could have been that they affected each other, and that would be more complicated -- if you had to take account of the way they affect each other that would require more work than when they don't affect each other at all.
But it didn't turn out that way.
It sounds like you are asking for a complete theory about electric fields that would have this result fall out of it. You could imagine "OK, THIS is what electric fields are like! Now I know.". 
You could get a theory like that, but it would have to be compatible with relativity theory, since the numbers come out right from that. People have a hard time envisioning relativity, and if you had an alternative that got the same results, it might likely be hard to envision that too.
It would only be a way to think about it. The math gets the right experimental results within experimental error. Concepts about what's happening with the math are useful for your intuition, and they are likely to suggest interesting applications of the math. 
But probably there will be multiple concepts that fit, with no way to show which of them is right. They're just ways to think about it that are compatible with the math.
The particular thing we're seeing here is that the forces that each charge puts on all other charges after a delay, do not change each other. They all act independently. That's what the math describes. 
A: Superposition principle has not been proven experimentally, it’s the other way around: experimental evidence suggested that the interaction between multiple electric charges could be modeled assuming the effect were incremental, so electrostatics has been developed with this feature in mind.
Superposition principle is, indeed, a principle (i.e. a postulate), which is justified only in a specific range of conditions, that is, whenever we can neglect nonlinear effects in the interaction between charges: macroscopically this is practically always verified, and it’s the reason of the success of the theory.
You can read the introductory chapter of Jackson (3rd edition) for further insight about this;
A: According to classical electromagnetism, the principle of superposition applies to electric fields because the Maxwell's equations are linear. Those equations hold the status of postulates in the classical treatment. And as far as normal day to day life is concerned, we know the classical equations work very well. Therefore, their implication that the fields can be superimposed is a direct consequence (not an assumption).
There is indeed a deeper meaning to this though. Superposition principle for electric fields implies that the presence of other charges does not affect the field of a charge. And although Quantum Electrodynamics (the more accurate EM theory) does not involve such things as forces and fields it does explain why that may be so. Photon, the mediator of EM force in QED, does not couple with itself. 
What does that mean? Let's say you have two charges. In QED, they interact with each other by exchanging photons. Classically, we think of each of them setting up a field and then each charge interacts with the field. Now, you introduce a third charge. According to QED, it will exchange photons with the first two charges but these photons will not affect the photons involved in the interaction between the first two charges. All the interactions add up (linearly). Classically, you say the fields setup by the first two charges have not been affected by the third charge.
There is a slight catch to this. While photons do not couple with each other directly they can interact with each other indirectly via vaccum polarization. An example of such an interaction is Delbrück Scattering. Fortunately for us such effects are considerably weaker when compared to the primary charge-photon coupling and therefore do not change our calculations too much.
Edit: I must clarify that QED does not explain why photons do not couple with each other. This is too an assumption. You may call this kicking the can down further and you won't be wrong. We just don't know why this is so.
