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The electric field of a straight charged wire is calculated when the wire is coated with a cylindrical insulation and is placed on the plane boundary between two dielectric media. The exact solution of the problem is derived in form of a rapidly convergent series. The technique used for the solution is based on the effective methods of the theory of functions of complex variables. The peculiarities of the electric field configuration are discussed. Some remarks are included concerning possible generalization of the solution to a system with multiple wires.