Hi my friends ,,

I having a problem and i tried to solve it as attached fig , I want you to verify the validity of my solution (because the choice questions is very precise)

 

BTW.. the mutual inductance LAW between two solenoides is an approximation,,
i found out it from the internet.

 

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A straight forward approach may be used in calculating self inductances with no regard to other factors. For mutual inductances; other inductors in proximity to the first, calculus should be used because the influencing factors are in 3 dimensions to the first. For the final word on self and mutual inductances, see Inductance Calculations by Professor Frederick Grover, 1946, ISBN 0486495779

Cheers, DPW [Everything has limitations...and I hate limitations.]

 

I'm guessing the OP is using simple ideal models for self & mutual inductance in which there is no leakage flux or partial self or mutual flux linkages. Such as one encounters for the infinitely long solenoid inductance model.

The multiple choice answers offered suggest this is perhaps the case.

The OP can rest assured the values obtained by them are OK in that context. Although, the supposed requirement for precision is debatable with respect to the answers both given & calculated.