It is clear by now if a power factor correction capacitor (a capacitance) is connected across the terminals of an induction motor the power factor looking from the source side improves.
Let's consider an example of a 100 HP motor. The incoming KW is about 80 KW and the power factor is about 0.85 for a 4 pole motor. Slower speed motors have more iron, they are in larger frames, therefore require more magnetizing current. This means a lower power factor. The recommended amount of capacitance to correct to 0.95 lagging is about 23 KVARs. To correct to 1.0 PF would require around 47 KVARs. This is not recommended as this would provide a slightly leading power factor at no load.
Let's think about the motor at no load. The only real load is the friction and windage, some core loss, and some I squared R loss, the motor speed is fairly close to the speed of the revolving field synchronous speed, either 1500RPM for 50 Hertz systems or 1800 RPM for 60 Hertz systems. The rotor has to slip to cut magnetic lines of flux or no torque is produced. If the capacitance provides the correct amount of magnetizing current the line current will be close to zero. The only load is Friction and Windage, etc. Everything is in balance. If the source is removed, the motor contractor opened, the voltage on the motors terminals will remain until the stored energy is used up in the losses of the motor friction and windage, the I squared R of the motor, and the capacitor losses. A motor with a shunt capacitor will also contribute more short circuit current than one without.
Under normal operation, that is with motor load, too much capacitance could result in high transient torques and motor terminal over voltage. These occur during switching events, opening and closing the contractor or momentary interruptions of source power.
Under load everything in the motor is balanced. There is just enough magnetizing current to supply the needed flux and just enough slip to provide the right amount of rotor current. A small change in load torque results in a small change in rotor current which changes the rotor slip and on and on. The counter EMF Hugh wrote about is also balanced in such a way to make the source voltage minus the counter EMF equal to the motor stator line current. The counter EMF is a result of the revolving magnetic flux on the turns in the stator winding.