A unique Fourier series approach to the problem of computing currents excited on a conducting bent wire enclosed in a shielded enclosure is presented. The wire is folded at right angle and oriented in a plane parallel to one of the cavity walls. Electromagnetic sources exterior to the cavity excite one end of the wire, while the other end of the wire within the cavity may have any arbitrary load conditions. The coupling between the two portions of the bent wire, which are perpendicular to each other, is taken into consideration. The formulation of this problem makes use of the theory of Fourier series to approximate the waveform of unknown current excited on the wire. Of course, the infinite Fourier series is approximated by a truncated Fourier cosine series in order to obtain an analytically simple solution. The number of Fourier series coefficients and the cavity modes are the key issues to the formulation. Selected numerical results in the form of current distributions are presented to illustrate the formulation. This formulation can easily handle any arbitrary load condition.