Q.Derive an expression for the capacitance of a spherical capacitor consisting of two concentric conducting spherical shells of radii $a$ and $b$ ($b>a$), and show that this expression reduces to the parallel plate capacitor formula when the gap $b-a$ is very small compared to $a$ and $b$.

Isolated conducting sphere of radius $R$ (a "solid" sphere capacitor, w.r.t. a hypothetical shell at infinity): $C=4\pi\epsilon_0R=R/k$, from $V=kQ/R$ at the surface. Two concentric conducting shells, inner radius $a$ (charge $+Q$) and outer radius $b$ (charge $-Q$) -- a "hollow" spherical capacitor: field and potential drop exist only between $a$ and $b$, giving $V=kQ(1/a-1/b)$ and $C= …