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

In real world, all objects obey Newton’s thirds law. A coil with current flowing within produces magnetic field that exerts force on the current of the coil itself. If the coil is not round, this force tends to make the coil round. But the total force on the coil is zero and the coil does not move as a whole. However, when this force is computed using the Lorentz force law, the total force is not zero. So, Newton is unhappy with Lorentz. In the following, we take the isosceles triangle coil ABC shown in Figure 1 and compute the total force numerically

Please read the article at
Unhappiness of Newton with Lorentz and triangular coil experiment
http://pengkuanem.blogspot.com/2013/05/unhappiness-of-newton-with-lorentz-and.html
or
http://www.academia.edu/3500211/Unhappiness_of_Newton_with_Lorentz_and_triangular_coil_experiment