= Solution
Put charges $+Q$ and $-Q$ on the concentric conductors. <Gauss's law> gives $E(r)=Q/(4\pi\epsilon_0r^2)$ between them, $a<r<2a$. The potential difference is
$$
\Delta V=\int_a^{2a}\frac{Q}{4\pi\epsilon_0r^2}\,dr
=\frac{Q}{8\pi\epsilon_0a}.
$$
The <capacitance> of this vacuum <spherical capacitor> is therefore
$$
\boxed{C=\frac{Q}{\Delta V}=8\pi\epsilon_0a.}
$$
The conductors are equipotentials; a uniform dielectric filling would replace $\epsilon_0$ by its <permittivity>.
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