Why is the formula for magnetic field not divided by length in this image?

[nabliat]

http://i26.tinypic.com/250tkyh.jpg

the formula for magnetic field
is like they show but its not divided by l
like they did

i can't see a reason why they present it that way
??

 

[gabbagabbahey]

You mean in the equation for $M$?

If so, $M$ is the mutual inductance and by definition,

$$\Phi_{\text{total}}=MI\implies M=\frac{\Phi_{\text{total}}}{I}$$

 

[nabliat]

no
i am asking about the previous step
when they found the magnetic field
and the expression has l in the denominator

why??

 

[gabbagabbahey]

Sorry, the lower case 'L' in your post looked a lot like an upper case 'i' the first time i read it...

$$\frac{N_b}{l}$$ would give you th number of turns per unit length in the solenoid, which is what $n$ represents in the version you are probably used to seeing: $B=\mu_0 n I$.

 

[nabliat]

thanks :)