I Guidance Requested on Inductance Formula for Solenoid

[warhammer]

In my textbook on EM, the formula for self inductance of a finite solenoid is given as:

L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid.

I am having trouble and extreme difficulty in trying to ascertain how this formula was derived in the book and what kind of geometry. They have not provided any explanations and simply stated the same.

I request guidance/hint from PF Members as to how this formula was derived.

 

[vanhees71]

Which textbook is it? Does it point to other textbooks/papers, where the formula is derived?

 

[tech99]

I believe that for a finite length solenoid there is a problem with calulating inductance and so there are several emprical formulas available.