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This letter considers the effect of the eccentricity on the static field and charge distribution for a circular aperture pierced by a long cylinder. The conformal mapping method is used to convert the problem of an eccentric aperture into that of a concentric aperture. The Weber transform, superposition principle, and mode matching are employed to calculate the static potential for this concentric problem. Numerical computations illustrate the behavior of potential distribution, surface charge density, and partial charges on the plane for various aperture eccentricities.