The pilot of the agricultural spray airplane reported that the airplane's fuel gauge was stuck and it provided an inaccurate indication of the fuel remaining. He thought there was about 30 minutes of fuel remaining, but the engine quit about 3 miles from the grass airstrip where he intended to land. He reported that the airplane experienced fuel exhaustion, and he executed a forced landing to a field. The airplane sustained substantial damage when it nosed over in a field. The inspection of the airplane in the field revealed no fuel in the fuel tank. No fuel was found in the hose from the electric fuel pump to the engine driven fuel pump.