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The ground state binding energy of a hydrogenic impurity in a coaxial cylindirical quantum well wire system subjected to an external electric field applied perpendicular to the symmetry axis of the wire system is studied within a variational scheme. Binding energy calculations were performed as functions of the inner barrier thickness and the electric field for two different impurity positions. The main result is that a sharp decrease in the binding energy, which may be important in device applications, occurs in certain conditions.