Electromagnetic problem
An analytical case is presented in order to show that the airgap Maxwell Tensor method is taking into account the Lorentz forces (sometimes called Laplace forces).
Lorentz force
According to the Lorentz force acting on a section L of the wire is given by:
Maxwell Tensor
According to the Maxwell Tensor method, the total magnetic force

Conclusion
Then the Lorentz’s forces and the Maxwell forces are equal in this case: