Spherical capacitor
= Spherical capacitor
{title2=$C=4\pi\epsilon_0ab/(b-a)$}
Two concentric conducting spherical shells of radii $a<b$ with charges $Q,-Q$ have an <electric field> only in the intervening vacuum: $E_r=Q/(4\pi\epsilon_0r^2)$ by <Gauss's law>. Integrating gives a potential difference $Q(1/a-1/b)/(4\pi\epsilon_0)$, and hence the displayed <capacitance>. The <electrostatic energy> is $Q^2/(2C)$, either by charging work or by integrating $\epsilon_0|E|^2/2$ over the gap.