# Why does magnetic flux decrease as turns increase in a coil but opposite is the case in magnetic circuits?

In magnetic fields, we have $$N \times I = \phi \times R$$ where $$\N\$$ is the number of turns, $$\I\$$ is the current, $$\\phi\$$ is the flux, and $$\R\$$ is the magnetic reluctance.

But in coils, we have $$N \times \phi = L \times I$$ where $$\L\$$ is the self-inductance, so $$\phi = LI/N$$

In the first case, more $$\N\$$ means more $$\\phi\$$.

In the second case, more $$\N\$$ means less $$\\phi\$$.

Why is this the case?

• How does self-inductance depend on N?
– jonk
Commented Aug 4, 2022 at 10:21
• L is Henry, better said Self-Inductance factor. Commented Aug 4, 2022 at 10:26
• Do you recall an $N^2$ factor as a proportional component to computing self-inductance L?
– jonk
Commented Aug 4, 2022 at 10:31
• I certainly do. Oh, it factors out the N in left Commented Aug 4, 2022 at 10:32
• Yeah, mathematic sums up. But is not there a more logical and intuitive appraoch than this? Commented Aug 4, 2022 at 10:42

$$L = \dfrac{\mu N^2 A}{d}$$
Where A is the cross sectional area of the inductor, d, is the mean path that flux travels and $$\\mu\$$ is the magnetic permeability constant.