In charged particle beam experiments, the electromagnetic signal produced at the beam injection point (conducting foil or aperture) by a fast‐rise beam will reflect off conducting boundaries (pipe walls) to produce constructive and destructive interference.B‐dot loop diagnostics can, in that case, give rather complicated signal histories that are difficult to interpret. An idealized, cylindrical model of a sudden rise beam on axis is solved analytically and shows, in the relativistic limit, how the interference is manifested. Results of the model corroborate and provide interpretation of corresponding PIC simulation results.B‐dot loop diagnostics of fast‐rise charged particle beams are most easily interpreted when the loops are close to the beam axis, or far downstream from the injection plane, and when frequency filtering of the signal is performed.