Using molecular dynamics simulations we compare the motion of a nano-swimmer based on Purcell's suggested motor with a time asymmetrical cycle with the motion of the same molecular motor with a time symmetrical cycle. We show that Purcell's theorem still holds at the nanoscale, despite the local structure and the medium's fluctuations. Then, with the purpose of both orienting the swimmer's displacement and increasing the breakdown of the theorem, we study the effect of an electric field on a polarized version of these swimmers. For small and large fields, the time asymmetrical swimmer is more efficient, as suggested by Purcell. However we find a field range for which Purcell's theorem is broken for the time symmetric motor. Results suggest that the breakdown of the theorem is arising from the competition of the orientation field and Brownian forces, while for larger fields the field destroys the effect of fluctuations restoring the theorem. arXiv:2001.03991v1 [cond-mat.soft]