what is the resulting mutual inductance

Question

Consider an ideal solenoid X that carries a current 2I. Another solenoid is wrapped around solenoid X resulting to a mutual inductance of 2M . If the current in X is halved, what is the resulting mutual inductance?

Answer 1

Mutual inductance M=NФ/i where N is number of turns of solenoid X, i is the current (2I) through it, and Ф is flux through each coil of outer solenoid. As given 2M=NФ/i

If current i will be changed (from i to i/2), then new M=4M. Pay attention that there is not change of N and Ф, and M is inverse proportional to current.