M2-brane probe no-force identity (${\mathcal{L}}_{\mathrm{static}}=-T_2$)

For $F={\mathrm{vol}}_{012}\wedge d{H}^{-1}$ and $F=dA$, choose $A=(1-H^{-1}){\mathrm{vol}}_{012}$. A parallel probe then has $q=-1$ in the supermembrane action, so its induced-volume term $-T_2{H}^{-1}$ and potential term $-T_2(1-H^{-1})$ add to a position-independent constant. This proves the cancellation without a weak-field approximation. An oppositely charged probe has no such cancellation.