New electronic phases often emerge in the proximity of a quantum critical point (QCP) - that is the point where the transition temperature of a collective phase transition is pushed to zero by varying some control parameter such pressure or composition. The bilayer ruthenate material Sr3Ru2O7 shows what appears to be a new "electron nematic phase" (ENP) near a critical magnetic field of 8 Tesla. The ENP is associated with the appearance of strong anisotropic tendencies in transport properties and an increased entropy at low temperatures. One microscopic explanation of the ENP is that it is due magnetic excitations which are strongly affected by an applied magnetic field. The present proposal is to check this by measuring the low frequency magnetic response in an applied field in the ENP.