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Evaluation of the electric field at the surface of a conductor, which is well described by the Poisson equation, is of great importance on many occasions in power systems. This paper proposes a collocation boundary element method where the unknown surface charge density function is assumed to be either azimuth independent or dependent. Detailed formulas, including the quadrature rules and how to accelerate the computation when the target point lies far away from the integral element, are proposed. Numerical examples are shown to confirm the convergence of the method, and manifest the great advantage for the evaluation of the electric field around slender conductors.