  As repeatedly speculated in the past, the linear polarization of the Cosmic
Microwave Background can be rotated via the Faraday effect. An economic
explanation of the recent Bicep2 observations, not relying on long-wavelength
tensor modes of the geometry, would stipulate that the detected B mode comes
exclusively from a Faraday rotated E mode polarization. We show hereunder that
this interpretation is ruled out by the existing upper limits on the B mode
polarization obtained by independent experiments at observational frequencies
much lower than the operating frequency of the Bicep2 experiment. We then
derive the fraction of the observed B mode polarization ascribable to the
Faraday effect and suggest a dedicated experimental strategy for its detection.
