Paradoxical Lorentz force internal to a triangle coil

Take a rigid triangle coil (Fixed on a wooden plate, yellow in the Figure 1), a current I flows in it. The 3 sides would feel a Lorentz force from the magnetic field of the other sides. These force are internal to the coil.

Now, put the side s₃ inside a ideal magnetic shield. So, the sides s₁ and s₂ would not feel the magnetic field from the side s₃ and the latter does not feel that from s₁ and s₂. What will be the total internal force on the triangle in this case?

The side s₃ would feel no force. The side s₁ would feel the Lorentz force F₁ from the side s₂ and the side s₂ the Lorentz force F₂ from s₁ respectively. So, the total internal force of the triangle coil is F₃= F₁+F₂. As the forces F₁ and F₂ are Lorentz forces, they are perpendicular to their sides and they make an angle between them. Their resultant force F₃ is non null.

If the total internal force is non null, any movement in the direction of the resultant force would do a work and create a energy. This is impossible because energy cannot be created.

So, the fact that the Lorentz force is perpendicular to the current violates the third Newton's law and the energy conservation law. This is the paradox of the internal Lorentz force.

This paradox is explained and solved in the document behind the link Paradoxes and Solutions.

The Lorentz force law presents some deficiencies. A study is in this document..
Paradoxes and Solutions