  We investigate the possibility for the SKA to detect and study the magnetic
fields in galaxy clusters and in the less dense environments surrounding them
using Faraday Rotation Measures. To this end, we produce 3-dimensional magnetic
field models for galaxy clusters of different masses and in different stages of
their evolution, and derive mock rotation measure observations of background
radiogalaxies. According to our results, already in phase I, we will be able to
infer the magnetic field properties in galaxy clusters as a function of the
cluster mass, down to $10^{13}$ solar-masses. Moreover, using cosmological
simulations to model the gas density, we have computed the expected rotation
measure through shock-fronts that occur in the intra-cluster medium during
cluster mergers. The enhancement in the rotation measure due to the density
jump will permit to constraint the magnetic field strength and structure after
the shock passage. SKA observations of polarised sources located behind galaxy
clusters will answer several questions about the magnetic field strength and
structure in galaxy clusters, and its evolution with cosmic time.
