Inductance of a coil with $10^4$ turns is $10\text{ mH}$ and it is connected to a dc source of $10\text{ V}$ with internal resistance of $10\ \Omega$. The energy density in the inductor when the current reaches $\left( \frac{1}{\text{e}} \right)$ of its maximum value is $\alpha\pi \times \frac{1}{\text{e}^2}\text{ J/m}^3$. The value of $\alpha$ is _________.
$(\mu_0 = 4\pi \times 10^{-7}\text{ Tm / A})$
