Physics Question from JEE Main 2026 · 22 January, Shift 1

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 $10 \, \Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha \pi \times \frac{1}{e^2} \, \text{J m}^{-3}$. The value of $\alpha$ is _____. $\left(\mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1}\right)$