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 $$ \alpha\pi \times \frac{1}{e^{2}}J/m^{3} $$. The value of $$ \alpha$$ is_______.
$$ (\mu_{o}=4\pi\times 10^{-7}Tm/A). $$