We investigate the Hall coefficient RH, resistivity, and magnetization of URu2Si2 and U(Ru0.96Rh0.04)2Si2 in the high field regime up to 45T to trace the electronic structure changes in both high and low temperature regimes. We find that at high temperatures above ∽7K, temperature- and field-dependent positions of RH maxima and magnetoresistance maxima coincide with a coherent temperature Tcoh at each field. These systematically decrease in temperatures with increasing fields and extrapolate to zero at the field-induced putative quantum critical point (QCP). This observation suggests a collapse of a new energy scale, i.e., a coherent temperature of a heavy quasiparticle band, at the putative field-induced QCP. At lower temperatures, we show there are discontinuous changes of the Hall number nH=1/RHe at the phase boundaries. This behavior illustrates that the phase formation is caused by first order reconstructions of the Fermi surface, which we interpret to the polarization of Fermi surface pockets seen in de-Haas van-Alphen (dHvA) measurements.