= Solution
The integral and differential forms of <Gauss's law> in vacuum are
$$
\oint_{\partial V}E\cdot n\,dA=\frac{Q_{\mathrm{enc}}}{\epsilon_0},\qquad
\nabla\cdot E=\frac\rho{\epsilon_0}.
$$
For an isolated spherical <conductor>, symmetry gives $E(r)=Q/(4\pi\epsilon_0r^2)$ outside and zero inside. Taking <electric potential> zero at infinity, $V(R)=\int_R^\infty E(r)\,dr=Q/(4\pi\epsilon_0R)$. Thus the <capacitance of an isolated conducting sphere> is
$$
\boxed{C=4\pi\epsilon_0R.}
$$
Charging from zero gives the <electrostatic potential energy>
$$
\boxed{W=\int_0^Q\frac qC\,dq=\frac{Q^2}{8\pi\epsilon_0R}=\frac12CV^2.}
$$
This is also the integral of <electric field energy density> $\epsilon_0E^2/2$ outside the sphere. The later insertion into a <coaxial cylindrical capacitor> conserves its <electric charge>, not its original isolated <electric potential>.
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