  This paper investigates the Faraday effect as a different source of B mode
polarization. The E mode polarization is Faraday rotated provided a stochastic
large-scale magnetic field is present prior to photon decoupling. In the first
part of the paper we discuss the case where the tensor modes of the geometry
are absent and we argue that the B mode recently detected by the Bicep2
collaboration cannot be explained by a large-scale magnetic field rotating,
through the Faraday effect, the well established E mode polarization. In this
case, the observed temperature autocorrelations would be excessively distorted
by the magnetic field. In the second part of the paper the formation of Faraday
rotation is treated as a stationary, random and Markovian process with the aim
of generalizing a set of scaling laws originally derived in the absence of the
tensor modes of the geometry. We show that the scalar, vector and tensor modes
of the brightness perturbations can all be Faraday rotated even if the vector
and tensor parts of the effect have been neglected, so far, by focussing the
attention on the scalar aspects of the problem. The mixing between the power
spectra of the E mode and B mode polarizations involves a unitary
transformation depending nonlinearly on the Faraday rotation rate. The present
approach is suitable for a general scrutiny of the polarization observables and
of their frequency dependence.
