Here we show Wilson lines do not necessarily exhibit Coulomb scaling laws in AdS/BCFT at zero temperature. The area difference between a surface that returns to the boundary, and one that plunges into the bulk, determines the potential between two quarks. This classic AdS/CFT calculation is extended to Wilson surfaces associated to general $(p-1)$-form symmetries in boundary conformal field theories (BCFTs) by embedding a Karch-Randall (KR) brane. Work done on the boundary charge under a dilatation determines the coefficient of this potential in closed form. Consequently, Coulomb law scaling in subregion size $\Gamma$ is recovered only above the critical angle for the brane, ${\theta }_{c,p}$, where the configuration is dilatation invariant. The potential between the two quarks (or defect operators) vanishes precisely when the surface connecting them ceases to exist at ${\theta }_{c,p}$. Thus operators are fully screened in this phase transition from Coulomb law to perimeter law, for which we compute the order parameter $C_p$ of the transition. At finite temperature a horizon breaks dilatation invariance, and so $p$-analogues of islands continue to exist below ${\theta }_{c,p}$.