I am currently learning about transformers in my physics class.

How does mutual inductance even apply here? The coils act as solenoids, and the field outside of a solenoid is 0, meaning that no emf should be induced in the opposing coil. We're also given equations such as,

The textbook claims that "The flux per turn ΦB is the same in both the primary and the secondary", which also doesn't make sense to me. How can the flux per turn be the same when the voltage is different in both circuits?

 

The textbook claims that "The flux per turn ΦB is the same in both the primary and the secondary", which also doesn't make sense to me. How can the flux per turn be the same when the voltage is different in both circuits?

The voltage/turn is the same on both sides. (not the volts but the V/T)

 

Fundamentals:

 

Also note that the flux is proportional to the primary volts (and inversely with frequency), not the current.
The flux value is basically independent of load current.