# 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.

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