📢Magnetic Stress Tensor via Field Tensors

The analysis of the magnetic field tensor demonstrates the power of tensor notation in physics, showing how its inherent anti-symmetry leads directly to the symmetry of its square, a necessary condition for a physical stress tensor. The derivation relies heavily on the Levi-Civita identity to compute the tensor product, yielding the key result, which links the fundamental magnetic field tensor to the standard vector dyadic product. Finally, by expressing the scalar field energy as a trace of the tensor product, the entire Maxwell stress tensor is converted into a form defined exclusively by the magnetic field tensor, ensuring mathematical consistency and demonstrating the elegance of field-based tensor formalisms.

Tensor Analysis of the Magnetic Stress Tensor | Proof and Derivationviadean on Notion