We have studied the transport process in the two dimensional electron gas (2DEG) in presence of a magnetic field and a dissipative environment at temperature T. By means of imaginary time series functional integral method we calculate the decay rates at finite temperature and in the presence of dissipation. We have studied decay rates for wide range of temperatures -- from the thermally activated region to very low temperature region where the system decays by quantum tunneling. We have shown that dissipation and impurity helps the tunneling. We have also shown that tunneling is strongly affected by the magnetic field. We have demonstrated analytical results for all the cases mentioned above.