The specific tensor notation for the Divergence Theorem (Gauss's Theorem) used in the derivation is:
$$ \int_V \partial_j A^j d V=\oint_S A^j d S_j $$
This notation is crucial because it allows the volume integral of the divergence of a rank-two tensor (or vector field, where $A^j$ are the components) to be directly converted into a surface integral. In the magnetic force derivation, the quantity $A^j$ is replaced by the expression for the Maxwell Stress Tensor components, $T^{i j}=\frac{1}{\mu_0}\left(B_j B_i-\frac{1}{2} \delta_{i j} B^2\right)$, enabling the conversion of the volume force integral to the final surface integral.
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