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 Ω. The energy density in the…

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