Electromagnetic Induction and Alternating Currents: JEE Main 2026 Physics question

Inductance of a coil with $10^4$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10\ \Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha\pi\times\frac{1}{e^2}\ \mathrm{J/m^3}$. The value of $\alpha$ is ______. ($\mu_0=4\pi\times10^{-7}$ Tm/A).