A point charge Q is located at the origin. Determine the...

The electric field at a distance $r$ from a point charge $Q$ is given by $E = \dfrac{Q}{4\pi\varepsilon_0 r^2}$.

The electrostatic energy density in the region is $u = \dfrac{1}{2}\varepsilon_0 E^2$.

The total electrostatic energy stored outside a sphere of radius $R$ is obtained by integrating the energy density over the volume from $r = R$ to $r = \infty$.

$U = \int_R^{\infty} u \, dV$

Substituting $u$ and the volume element $dV = 4\pi r^2 dr$:

$U = \int_R^{\infty} \dfrac{1}{2}\varepsilon_0 \left( \dfrac{Q}{4\pi\varepsilon_0 r^2} \right)^2 4\pi r^2 dr$

$U = \int_R^{\infty} \dfrac{Q^2}{8\pi\varepsilon_0 r^2} dr$

$U = \dfrac{Q^2}{8\pi\varepsilon_0} \left[ -\dfrac{1}{r} \right]_R^{\infty}$

$U = \dfrac{Q^2}{8\pi\varepsilon_0 R}$