Upper limits have been obtained for the size of any asymmetry in the power dissipation between the current entry and exit points of a Si MOSFET in a quantizing magnetic field. Measurements have been made for power inputs between 0.3 and 2000 mu W and for filling factors between 4 and 32. These show that if the total power dissipated I²R_H is shared between the current entry and exist points in proportions (50+or-x)%, then for example at 8 mu W, x<or=1.35 for i=8. No evidence was obtained for any additional dissipation close to the electron entry point near to quantum Hall breakdown.