The object of this article is to compute the overall Lorentz force a coil exerts on itself. For doing so, we cut the coil into 2 parts and compute the forces on each part, then sum the 2 forces. Naturally, many physicists suggest to compute the force by integrating the Lorentz force on the wire produced by the magnetic field in the vicinity of the wire, in Figure 1 (1).

Please read the article at
Computation of the self force of a coil
http://pengkuanem.blogspot.com/2013/05/computation-of-self-force-of-coil.html
or
http://www.academia.edu/3631539/Computation_of_the_self_force_of_a_coil