The logic of the self inductance formula

[nabliat]

$$M_{12}=\frac{N_2\phi _{12}}{I_1}$$

i need to remmeber it

but i can't see the logic of
the formula
??

 

[roam]

$$M_{12}=\frac{N_2\phi _{12}}{I_1}$$

i need to remmeber it

but i can't see the logic of
the formula
??

I thought the formula looked something like: $$\frac{\mu_{0}N^2 A}{l}$$. A is the cross section & magnetic field inside the solenoid is $$B=\mu_0 NI/l$$, flux through one loop is $$BA=\mu_0 N IA/l$$ and $$\Phi= \mu_0 N^2 I A/l$$ is the total flux. The inductance is just total flux divided by current.