Скачать или смотреть Magnetic Tensor Defines Tension and Pressure

Demo:    • how the magnetic stress tensor decomposes ...  

Derivation sheet: https://viadean.notion.site/Tensor-An...

Summary: The Maxwell Stress Tensor ($T_{ik}$) is derived from the magnetic field tensor ($F_{ij}$), which is defined by the anti-symmetric relationship $F_{ij} = \varepsilon_{ijk} B_k$. A key mathematical takeaway is that the product $F_{ij} F_{jk}$ is symmetric in its free indices and provides a method to express the Maxwell Stress Tensor in terms of the magnetic field tensor rather than just vector components. Physically, this relationship represents a dynamic interplay between isotropic energy and field direction, where $F_{ij} F_{jk}$ is formed by subtracting the directional dyadic product ($B_i B_k$) from the uniform isotropic term ($B^2 \delta_{ik}$). This mathematical structure translates into tangible mechanical forces: the isotropic term creates pressure perpendicular to field lines, while the dyadic term creates tension along them. Ultimately, the resulting tensor demonstrates that magnetic fields exert a net pulling force (tension) along their direction and a net pushing force (compression) perpendicular to it, defining their physical impact on the surrounding media.