= Image line charge for a grounded conducting cylinder
{title2=$r_{\rm image}=a^2/b$}
A real infinite <line charge> $\lambda$ lies at distance $b>a$ from the axis of a grounded conducting cylinder of radius $a$. An image line $-\lambda$ at radius $a^2/b$ lies inside the excluded conductor. On the circle, real and image distances obey $r_1/r_2=b/a$, so $\phi=(\lambda/(2\pi\epsilon_0))\ln[(b/a)r_2/r_1]$ vanishes there. The image field solves the physical exterior problem with bounded far potential. Its additive constant matters; the interior image field is not a physical field inside the conductor.
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