In this paper , we consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylindrical conductor.If the conductor is an open arc in R~2,we can consider the problem of scattering by an open arc in R~2.We assume that the arc is divided into two parts with different boundary value conditions.So it can be considered as the following scattering problem of the Helmhotz equation.The v denotes the unit normal to the corresponding boundary,U is total wave.u~i is incident wave, d denotes the incident direction,besides,the scattering wave must satisfy Sommerfeld's radiation condition.Applying potential theory,the problem can be reformulated as a boundary integralsystem.We obtain the existence and uniqueness of a solution to the system by using Fredholm theory.