Inductance per unit length near the middle of a long solenoid is $\left(\mu_0=\right.$ permeability of free…
Inductance per unit length near the middle of a long solenoid is $\left(\mu_0=\right.$ permeability of free space, $\mathrm{n}=$ number of turns per unit length, $\mathrm{d}=$ the diameter of the solenoid)
$\mu_0 \pi\left(\frac{\mathrm{nd}}{2}\right)^2$
$4 \mu_0 \pi\left(\frac{\mathrm{nd}}{2}\right)$
$\left(\frac{\mu_0 \pi \mathrm{nd}}{2}\right)$
$\frac{4 \mu_0 \pi}{n^2 d^2}$
Solution
The inductance long solenoid is
$\begin{aligned}
& \mathrm{L}=\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{l} \\
& \mathrm{~L}=\mu_0\left(\frac{\mathrm{N}}{l}\right)^2 \times \pi \times \frac{\mathrm{d}^2}{4}
\end{aligned}$
$\therefore \quad$ The inductance per unit length near the middle of a long solenoid is:
$\frac{\mathrm{L}}{l}=\mu_0 \pi\left(\frac{\mathrm{nd}}{2}\right)^2 \quad \ldots .\left(\because \frac{\mathrm{N}}{l}=\mathrm{n}\right)$