At a distance $r$ from a charge $e$ on a particle of mass $m$ the electric field value is $E=e / 4 \pi \varepsilon_{0} r^{2}$. Show by integrating the electrostatic energy density over the spherical volume of radius $a$ to infinity and equating it to the value $m c^{2}$ that the 'classical' radius of the electron is given by
$$
a=1.41 \times 10^{-15} \mathrm{~m}
$$