I have proven theoretically that the Lorentz force internal to a coil is not zero (several proofs are in the references). But theoretical proofs are too long to read and too complex. I give here a numerical computation of the Lorentz force internal to an asymmetrical coil; the computed force is not zero.

Please read the article at
Numerical computation of the Lorentz force internal to an asymmetric coil
http://pengkuanem.blogspot.com/2013/04/numerical-computation-of-lorentz-force.html
or
http://www.academia.edu/3386868/Numerical_computation_of_the_Lorentz_force_internal_to_an_asymmetric_coil