in an induction motor if airgap is increases then power factor of the motor gets decreases because the motor draws more magnetizing current which lags the voltage by a more angle. if the angle b/w voltage and current is more then the power factor will be less.
power factor will decrease and will be lagging . because increase in airgap causes stator winding to draw more magnetization current which causes total resultant current to Lagg more behind applied voltage and finally power factor will decreas
if air gap increases the magnetising current Im draws from the supply increases .the Im is inversely proportional to the power factor,from this Im increases p.f decreases