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We derive asymptotic expansions of the current, the electrostatic capacity,and the far-field of the electrostatic potential resulting from smallperturbations in the shape of an isolated conductor with$\mathcal{C}^2$-surface. Our derivation is rigourous by using systematic way,based on layer potential techniques and the field expansion (FE) method. Wethen use these results to study the sensibility analysis of the firsteigenvector of the $L^2$-adjoint of the Neumann-Poincar\'e (NP) operator withrespect to small perturbations in the surface of its domain.

Sensitivity Analysis of the Current, the Electrostatic Capacity, and the  Far-Field of the Potential with Respect to Small Perturbations in the Surface  of a Conductor