= Solution
For a smooth isolated <conducting sphere>, <Gauss's law> gives the surface <electric field> $E_s=Q/(4\pi\epsilon_0a^2)$ and <electric potential> $V=Q/(4\pi\epsilon_0a)=aE_s$. At the specified <dielectric strength>, $V_{\max}=3.0\times10^3\ \mathrm V$. The <capacitance of an isolated conducting sphere> is $C=4\pi\epsilon_0a$, so its <capacitor energy> is
$$
U_{\max}=\frac12 C V_{\max}^2=2\pi\epsilon_0a^3E_s^2
=\boxed{5.0\times10^{-7}\ \mathrm J\simeq0.50\ \mu\mathrm J.}
$$
This is the ideal <breakdown-limited energy of a conducting sphere>, taking air's <permittivity> approximately equal to <vacuum permittivity> and neglecting nearby objects and surface irregularities. The <vacuum permittivity> used numerically is $8.8542\times10^{-12}\ \mathrm{F\,m^{-1}}$.<Fundamental Physical Constants — Complete Listing by National Institute of Standards and Technology and others>[2022 CODATA adjustment, vacuum electric permittivity entry]{ref}
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