= Uniform electric field in an off-axis cylindrical cavity
{title2=$\mathbf E=\rho\mathbf a/(2\epsilon_0)$}
Remove an axial cylindrical hole, wholly contained in an infinite insulating cylinder with uniform fixed <charge density> $\rho$. Let $\mathbf a$ point from the original axis to the hole axis. The <superposition principle> replaces the removed material by a cylinder of <charge density> $-\rho$. At any point $\mathbf r$ inside the hole, the two interior <electric fields> add to $\rho[\mathbf r-(\mathbf r-\mathbf a)]/(2\epsilon_0)=\rho\mathbf a/(2\epsilon_0)$. The result is uniform throughout the hole, even when the hole is not concentric; it does not apply to a hole in an <electrical conductor> whose <electric charges> can redistribute.
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