= Radial magnetic induction scalar
{title2=$P=\mathbf B\cdot\mathbf x$}
For <solenoidal> velocity and <magnetic field>, with constant <magnetic diffusivity> $\eta$, the <resistive induction equation> implies
$$
\partial_tP+\mathbf u\cdot\nabla P=\mathbf B\cdot\nabla Q+\eta\Delta P,\qquad Q=\mathbf u\cdot\mathbf x.
$$
The <product rule> gives $D_tP=\mathbf x\cdot D_t\mathbf B+\mathbf u\cdot\mathbf B$ and $\Delta P=\mathbf x\cdot\Delta\mathbf B+2\nabla\cdot\mathbf B$. Consequently the radial velocity, through $Q$, is the source term for the radial <magnetic field>.
// Target: fluid-mechanics.bigb
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