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A calculation of the ground‐state energy of an exciton confined in a cylindrical quantum wire in the presence of a uniform magnetic field is reported as a function of wire radius, using a variational approach. It is assumed that the magnetic field is applied parallel to the axis of the wire. The calculations have been performed using a suitable variational wave function taken as a product of the appropriate confining confluent hypergeometric functions and a hydrogenic function for infinite and finite confining potentials. For a given value of the magnetic field, the binding energy is found to be larger than the zero‐field case. This behavior is explained in terms of an average electron‐hole separation, which depends on the wire radius, and the magnetic‐field strength. © 1995 American Institute of Physics.