Force on conductor due to current in it We say that the magnetic field produced by current carrying conductor produces no force on itself but I am not able to understand this simple argument.
Consider a long current carrying conductor.We observe that any small part of the wire has electrons in it which produce magnetic field independently.Now my question is at any other place in the conductor,electrons lie and therefore they must experience a force due to magnetic field produced by electrons in that small part of the wire which leads us to conclude that the conductor as a whole experiences force?Where lies the fallacy in my reasoning?
 A: The magnetic field due to a small element of current is given by the Biot-Savart Law:
$$ B(z) = \frac{\mu_0}{4\pi} I \int \frac{d\textbf{l'}\times \textbf{r}}{r^2} dr= \frac{\mu_0}{4\pi} I \int \frac{dl'}{r^2} \sin\theta dr $$
Which is basically the found using the cross product of the direction to which you’ll measure the field and the direction of the current. Notice that along the wire the cross product will be of two parallel vectors are direction you’re measuring along and current are parallel as $\theta$ is 0 so $sin(\theta)$ is 0. Hence there is no magnetic field in any part of the wire and hence the electrons in the wire don’t experience any force and the wire can be at equilibrium.
Note: This wire is a thin wire and it can work for both finite and infinite lengths of the wire. I am ignoring any drastic effects of Joule-Heating due to power dissipation of the resistance of the wire as I assume the current is not as high. But nevertheless even with a high current, it would not experience at least any magnetic forces as there is no field inside the wire. 
A: 
We say that the magnetic field produced by current carrying conductor produces no force on itself 

We most certainly not NOT say that. Here is the image of a copper conductor that had a strong current in it. This was part of testing that followed the realization that lightning rods were crushed in this fashion.
Someone will complain that this is a hollow conductor and claim it does not apply. However, I know of this image because I used it as an illustration of the Lorentz force in a plasma, which was used as a fusion confinement system in the 1950s. The same technique, with limits, remains in use in the tokamak designs like ITER. The plasma columns are continuous, not hollow.
Now someone will complain that it is a fluid, and so on.

A: A conductor with a current travelling through it experiences no net magnetic force. Individual pieces can indeed experience a force, it's just the sum of all these forces that adds up to zero.
This is obvious if you think about conservation of momentum, since if an isolated conductor with a current through it feels a net force its momentum will change.
A: Before reading: this is just a classic explanation, it is not used q.m.
Think to this experiment: an electron is moving through the empty space. There is an external generic electromagnetic field which produces a force on it. You are an observer who measures electron's speed $\mathbf{v}(t)$. It means that you always measure an electric and a magnetic field 
respectively due to the charge of the electron and to its speed: $\mathbf{E}=\mathbf{E}(x,y,z,t)$; $\mathbf{B}=\mathbf{B}(x,y,z,t)$. If you maesure  these two fields on the point in which instantly is situated the electron you find $\mathbf{E}=\mathbf{B}=\mathbf{0}$, it means that the electron doesn't auto-influence his motion, because it can't see the fields it generates. Now if you put another electron, the previous considerations stay true, but now the two electrons see one the fields that the other one generates, so they reciprocally influence their motion. You can solve some equations and get the two trajectories. You can consider a system with n electrons. If you want to know the total force acting on the system of the n electrons at a certain time, you have to sum all the forces. But the sum of the internal forces of the system is zero (third principle). So the only force that acts on the system of n electrons is the sum of all the forces due to the external electromagnetic field, on each electrons. This shows that the total force acting on the system just depends on the the external electromagnetic field, and it is zero if the external field is zero. If you have a current carrying conductor the electrons which make the current don't generate a force on the conductor, for this you need an external field.Hope it's clear.    
