Responses
Introduction
Physical quantity to optimize  Formula  Entity 

Flux flowing through faces 
$\phi =\frac{L}{S}\int {A}_{z}dS$

On a face belonging to a coil conductor region 
Flux flowing through a line 
$\phi =L\left({A}_{z}\right({n}_{1}){A}_{z}({n}_{2}\left)\right)$

On a line 
Sum of the fluxes of selected coils 
$\phi =\sum _{i=1}^{n}{\phi}_{i}=L\sum _{i=1}^{n}{N}_{Si}\int {A}_{z}dS$

On one or several coil conductor components 
Force computed with the integral of Pn on a path 
$Fm=L\int \frac{{B}_{n}^{2}{B}_{t}^{2}}{{\mu}_{0}}dl$

Based on the Maxwell tensors approach, this method requires a
path in a front of a piece of iron (plunger for an actuator,
stator tooth ...) Attention: This method is valuable
only along a path in a air or vaccum region.

Torque computed with the integral of Pt on a path 
$Tm=LpR\int \frac{{B}_{n}{B}_{t}}{{\mu}_{0}}dl$

Based on the Maxwell tensors approach, this method requires a
path in the airgap of a rotating machine, on the stator side as
depicted in th following picture: Attention: This method is valuable only along a path in a air or
vaccum region.

Volume of 2D faces  On faces 