Question: We all have elaborative discussion in physics about classical mechanics as well as interaction of particles through forces and certain laws which all particles obey.

I want to ask,Does a particle exert a force on itself?

**EDIT**

Thanks for the respectful answers and comments.I edited this question in order to make it more elaborated.

I just want to convey that I assumed the particle to be a standard model of point mass in classical mechanics. As I don't know why there is a minimum requirement of two particles to interact with fundamental forces of nature,in the similar manner I wanted to ask does a particle exerts a force on itself?

Answer: 
This question is never addressed by teachers, altough students start asking it more and more every year (surprisingly). Here are two possible arguments.

1. A particle is meant to have 0 volume. Maybe you're used to exert a force on yourself, but you are an extended body. Particles are points in space. I find it quite hard to exert a force on the same point. Your stating that the sender is the same as the receiver. It's like saying that one point is gaining momentum from itself! Because forces are a gain in momentum, after all. So how can we expect that some point increases its momentum alone? That violates the conservation of momentum principle.
2. A visual example (because this question usually arises in Electromagnetism with Coulomb's law):

$$\vec{F}=K \frac{Qq}{r^2} \hat{r}$$

If $r=0$, the force is not defined, what's more, the vector $\hat{r}$ doesn't even exist. How could such force "know" where to point to? A point is spherically symmetric. What "arrow" (vector) would the force follow? If all directions are equivalent...
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> The difficulties presented by this problem touch one of the most fundamental aspects of physics, the nature of the elementary particle. Although partial solutions, workable within limited areas, can be given, the basic problem remains unsolved. One might hope that the transition from classical to quantum-mechanical treatments would remove the difficulties. While there is still hope that this may eventually occur, the present quantum-mechanical discussions are beset with even more elaborate troubles than the classical ones. It is one of the triumphs of comparatively recent years (~ 1948–1950) that the concepts of Lorentz covariance and gauge invariance were exploited sufficiently cleverly to circumvent these difficulties in quantum electrodynamics and so allow the calculation of very small radiative effects to extremely high precision, in full agreement with experiment. From a fundamental point of view, however, the difficulties remain.
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John David Jackson, Classical Electrodynamics.