For an infinite vacuum-filled solenoid we know:
B=mu0 N I
where N=turns per length and each turn carrys current I
Note NI=j is the surface current 9sometimes called K) with units A/m
A was given (and checked) in B2.pdf 3d
Consider (and calculate) three different ways of finding the energy per length of the solenoid:
eq 12-11 (where L is calculated from the flux)
eq 12-13b (convert the J dV to j dA -- surface current.area)
eq 12-15
All should of course produce the same answer!