= Charged sphere inside a neutral coaxial capacitor
{title2=$\Phi_b=\frac{2RV_0}{l}\log(a/b)$}
An isolated <conducting sphere> of radius $R$ initially at potential $V_0$ has charge $Q=4\pi\epsilon_0RV_0$. Inserting it without contact into the hollow inner conductor of a long <coaxial cylindrical capacitor> conserves that charge. The neutral inner conductor acquires $-Q$ on its cavity wall and $+Q$ outside. With the outer conductor grounded, the annular <electric field> is $Q/(2\pi\epsilon_0lr)$ and the inner potential is the displayed result. The original <electric potential> is not conserved. End effects are neglected; exact cavity fields are geometry-dependent.
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