= Insulating boundary condition for the radial magnetic scalar
{title2=$[P]=[\partial_rP]=0,\quad\Delta P_{\mathrm{ext}}=0$}
At a spherical interface with an insulating exterior, equal <magnetic permeability> on both sides and no surface current, all components of the <magnetic field> are continuous. The <solenoidal magnetic-field constraint> then makes $P=\mathbf B\cdot\mathbf x$ and $\partial_rP$ continuous. A current-free exterior has $\Delta P=0$. For an isolated field decaying at infinity, its degree-$l$ <spherical harmonic> satisfies $\partial_rP_{lm}=-(l+1)P_{lm}/a$ at a sphere of radius $a$. This <boundary condition> incorporates the exterior field without setting the radial field to zero.
// Target: fluid-mechanics.bigb
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