Why Does Ampere's Law Use BL Instead of B(2L) for a Solenoid?

[cragar]

Lets take the infinite solenoid for example. Where we wrap wire around a pipe with current I.
We make our amperian path a rectangle, half inside the solenoid half out.
This site has the diagram I am talking about, a 1/4 way down the page.
http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter31/chapter31.html
This is probably a dumb question but why is it BL=(mu)NI
why is it not B(2L)=(mu)NI
It seems to me that it would be 2L because for our box we had to go all the way around to enclose the current.

 

[Doc Al]

It seems to me that it would be 2L because for our box we had to go all the way around to enclose the current.

But there's no field outside the solenoid, so that extra L does not contribute to the integral.

 

[cragar]

ok thanks so we are counting the L inside the solenoid.