Just analyze the equations carefully. And look at the raw parameters that make up the inductance of a solenoid. For instance I just noticed we completely ignored coil length so far. If you have two coils on top of each other, with the same amount of windings but one longer than the other. When energizing the short one and opening the switch and letting the long one collect the inductive energy what you did is instantly and effortlessly double the length, this would halve the flux, so conservation of flux kicks in and doubles current. Since inductive energy is linearly proportional to 1/length as well you should see an increase.





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