Let me take step back and ask this question:
What would happen to the flux in the magnetic core if the second coil is removed? Does only the leakage flux remain, or would some flux still flow through the whole core?
I have a very basic question regarding mutual inductance.
Consider a basic square loop with two coils wound on opposite sides from each other, with coil one excited while coil two si left open circuited. The total flux linking coil 1 is
Φ11 = Φl1+Φ21
where
Φ11 is the total flux...
If this is true, then dots and voltages aside, kevinf should be correct in his statement that the "17jI1" and "17jI2" referenced later should be "-17jI1" and "-17jI2."