First lets look at magnetizing current. That magnetizing current is at grid frequency, so it creates a flux which induces a "magnetizing" emf in the stator winding at grid frequency. The magnitude of magnetizing current adjusts so that the associated induced voltage is roughly equal/opposite to applied voltage. (the "opposite" terminology arises from tracing a loop where voltages sum to zero...some would prefer to say it's the same voltage).
If the motor is at no-load, that's all you've got, simple story.
If you add a load to the motor, then the rotor slows down, which results in slip and current in the rotor. This rotor current and associated flux creates a deviation in the emf (which was previously balanced by magnetizing emf), such that a roughly equal/opposite stator load-component current is required to roughly cancel the emf from rotor current to restore total emf equal/opposite to of applied voltage.
Both the rotor and load-component stator currents (and associated emf's) mentioned above have their fundamental (working) component at grid frequency.
Why is the rotor component at grid frequency? Roughly speaking: the rotor speed is Fsync*(1-s), the frequency of current in the rotor (in rotor frame of reference) is given by s*Fysnc, and when we look at how that emf appears when seen in stator frame of reference, we have to add together rotor speed and rotor frequency to give Fsync*(1-s) + s*Fysnc, = Fsync. i.e. fundamental/working rotor current and emf as seen in the stator reference frame is at grid frequency.
Since the stator load component emf is generated in response to rotor emf, it also has the same frequency.
If you consider effect of slotting, there are other frequencies to consider, but above focused on the "fundamental/working" component.
Voltage associated with leakage reactances and stator winding resistance were omitted from above discussion for simplicity.
The term emf I think has been debated before in some circles of the forums. For my purposes it is the same as "induced voltage"
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(2B)+(2B)' ?