Faraday rotation, which gives us the vector integral of 
B.dl
along the line of sight, is another important probe of
the IGM. Work to date has shown us that the centers of cooling flow
clusters have surprisingly large magnetic fields. Allowing for the
uncertainties of the number of field reversals along the line of
sight, the magnetic energy density in these regions could easily be as
high as the thermal energy density. The structure of the field is
probably very complex and is consistent with predictions of dynamo
models.
The enhanced VLA will open up new parts of parameter space for such
studies. At high frequencies, the increase in sensitivity will let us
probe sources in clusters which so far are completely
depolarized. These sources may have extreme rotation measures
for which the differential rotation over the synthesized beam or
across the observing band completely depolarizes the emission.
Adding the 2.4 GHz band will allow smaller Faraday rotations to
be detected by providing a critical part of 
space between
1.4 and 4.9 GHz.
Finally the increased sensitivity and the expected improvement in the systematics caused by the IF system of the current VLA should allow many more sources to be studied in Faraday rotation. This will allow much more complete imaging of the Faraday rotation along different paths through a cluster.
Imaging both the diffuse radio halos and the Faraday rotation seen through different parts of clusters should give us a clear picture of the importance of magnetic fields in clusters of galaxies and at a wide variety of different densities. This will be a major contribution of an enhanced VLA to extragalactic physics.