Final answer:
No, the oscillating magnetic field of one beam does not cause Faraday rotation in the other beam.
Step-by-step explanation:
When a vertically polarized beam of laser light passes through a horizontally polarized beam of laser light, it does not cause Faraday rotation in the other beam. Faraday rotation occurs when the polarization of light is rotated due to the presence of a magnetic field.
However, in this case, the beams are already polarized in different directions and the interaction between them does not result in Faraday rotation.