Stimulated bremsstrahlung in an undulating electric field in the lasing beam direction (electric wiggler) was shown to be possible from the quantum-mechanical viewpoint. Herein, this possibility is scrutinized from the viewpoint of classical electrodynamics. It is found that if stimulated bremsstrahlung in a transverse undulating magnetic field (magnetic wiggler) occurs, stimulated bremsstrahlung in the electric wiggler must also occur. We further show that a free electron laser (FEL) using a magnetic wiggler to provide a catalyzer field for stimulated bremsstrahlung cannot serve as a practical FEL operating in the soft x-ray region from both theoretical and experimental viewpoints. On the other hand, we demonstrate that the FEL using a traveling wake field in a two-beam elliptical pill-box cavity is well suited as a source of coherent radiation in the soft x-ray region.