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This problem has been bothering me for weeks. I read previous posts on this forum on topic of Maxwell stress tensor but still could not find what is wrong.

I'm trying to calculate the repelling force between two magnet rings with one levitated above the other. I defined a force variable for the top ring. COMSOL (AC/DC 3.3) gives "topring_nTz_emnc" as the surface force density at the boundaries of the top ring for calculating z-component of the force.

On the other hand, I manually defined elements of the Maxwell stress tensor as Global Expressions

T =(1/mu0)* [ Bx^2-0.5*|B|^2, BxBy, BxBz ;
ByBx, By^2-0.5*|B|^2, ByBz ;
BzBx , BzBy, Bz^2-0.5*|B|^2 ]
= [Txx, Txy, Txz;
Tyx, Tyy, Tyz;
Tzx, Tzy, Tzz];

Since I need to compute the z-component of the force, I used the Boundary Integration Coupling variable to calculate

Fz = int{nx*Tzx+ny*Tzy+nz*Tzz} dA

for each boundary of top ring. [nx ny nz] is the outward surface normal.

Here, nx*Tzx+ny*Tzy+nz*Tzz is also surface force density, which should agree with "topring_nTz_emnc" that is automatically generated by COMSOL.

However, I am getting different results. For some of the boundary surfaces (e.g. the inner and outer cylindrical faces of the top ring),

nx*Tzx+ny*Tzy+nz*Tzz

does not agree with

topring_nTz_emnc.

Any hints on what may have gone wrong?

Thanks,
Zhiyong