...$\nabla {\vec B} \ne 0$

As a matter of fact, if ${\vec B}$ and/or $\nabla {\vec B}$ are zero, then S₂ = 0 (S₂ is defined after Eq. (44)). Once S₂ is zero, it is impossible to solve Eq. (45) in the way shown in Eq. (46). This is why S₂ should be non-zero. Hence, if there is no magnetic field, ${\vec B}= 0$, these formulas are not applicable.

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