📢Magnetic Force Transmission via the Stress Tensor

Transforming the magnetic force integral is the conceptual shift from action-at-a-distance to the idea that the force is conveyed entirely by the Magnetic Stress Tensor acting on the boundary surface. This rank-two tensor describes the momentum flux exerted by the magnetic field across that boundary, allowing the total force to be calculated simply by measuring the magnetic field on the surface. Physically, the tensor's components reveal the dual nature of these field mediated stresses: the off-diagonal terms represent shear stresses that pull the surface diagonally, while the diagonal terms represent a uniform outward pressure exerted perpendicular to the field lines.

Conversion of Total Magnetic Force to a Surface Integral via the Maxwell Stress Tensor | Proof and Derivationviadean on Notion