Simply Solenoids

The self inductance $L$ of a solenoid is given by,

$L = \mu_{0} N^{2} \pi r^{2} l$ (1)

Let, $d$ be the length of the wire needed, for a solenoid

$d = 2 \pi r N$

$d^{2} = 4 \pi^{2} N^{2} r^{2}$

$\frac{d^{2}}{4 \pi} = \pi N^{2} r^{2}$ (2)

Substitute (2) to (1),

$L = \mu_{0} \frac{d^{2}}{4 \pi} l$

$L = 4 \pi \times 10^{-7} \times \frac{d^{2} l}{4 \pi}$

$L = d^{2} l \times 10^{-7}$

$10^{-3} = d^{2} l \times 10^{-7}$

$10^{4} = d^{2}$

$d = \boxed{100}$