🎬Visualizing the Magnetic Stress Tensor is highly illustrative of how magnetic fields exert forces

The magnetic stress exerted on a volume by a uniform magnetic field is fundamentally a combination of two independent stresses: tension and pressure. The Shear Term ( $B _i B_j$ ) acts as a tensile force, causing the material to stretch and elongate precisely along the direction of the magnetic field lines. Conversely, the Pressure Term ( $\frac{1}{2} \delta{i j} B ^{ 2 }$ ) acts as an isotropic pressure, causing the material to compress and squeeze inward perpendicular to the field lines. The resulting total magnetic force felt by a magnetized volume is the superposition of these two effects, which typically leads to a characteristic prolate, or football-shaped, deformation.

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