How much length of a very thin wire is required to obtain a solenoid of length ${\mathcal{l}}_0$ and inductance L

Suppose solenoid has N turns, each of radius r and length of wire is l.

Its self-inductance, $\mathrm{L}=\frac{{\mathrm{\mu }}_0{\mathrm{N}}^2\mathrm{A}}{{\mathcal{l}}_0}=\frac{{\mathrm{\mu }}_0{\mathrm{N}}^2{\mathrm{\pi r}}^2}{{\mathcal{l}}_0}$   .... (i)
Also, length of the wire, $\mathcal{l}=\mathrm{N}\times 2\mathrm{\pi r}$ 

$\Rightarrow {\mathrm{N}}^2{\mathrm{r}}^2=\frac{{\mathcal{l}}^2}{4{\mathrm{\pi }}^2}$      .... (ii)
From equation (i) and (ii)  , $\mathcal{l}=\sqrt{\frac{4\mathrm{\pi L}{\mathcal{l}}_{\mathrm{o}}}{{\mathrm{\mu }}_{\mathrm{o}}}}$