The energy spectrum of an electron confined near a current-carrying core is obtained as a function of the azimuthal
applied magnetic field within the effective-mass approximation. The double degeneracy of the non-zero electron's axial
wave number (kz) states is lifted by the current-induced magnetic field while that of the non-zero azimuthal quantum
number (m) states is preserved. A further analysis is the evaluations of the oscillator strengths for optical transitions
involving the lowest-order pair of the electron's energy subbands within the dipole approximation. The radiation field is
taken as that of elliptically polarized light incident along the core axis. In this polarization and within the dipole
approximation, the allowed transitions are only those governed by the following specific selection rules. The azimuthal
quantum numbers of the initial and final states must differ by unity while the electron's axial wave number is conserved.
The azimuthal magnetic field is also found to lift the multiple degeneracies of the kz=0 interaction integrals as well as
those of the oscillator strengths for optical transitions.