For a 40 amp breaker, the recommended wire size is 8 AWG. This is the American Wire Gauge standard used in the United States. However, if the wire runs for a long distance, a thicker wire may be needed to accommodate voltage drop. For cables running over 100 feet, 6-gauge copper wire or 4-gauge aluminum wire is recommended, and for cables running over 200 feet, 4-gauge copper wire or 2-gauge aluminum wire is recommended. It is important to note that 10 AWG and 12 AWG copper wires are not suitable for 40-amp circuit breakers, as they have 35 Amp and 25 Amp wire ampacity, respectively.