= Insertion barrier of a charged polymer
{title2=$F(x)=fx-qEx^2/2$}
If only the inserted <length> $x$ feels a uniform inward <electric field>, its charge experiences <force> $qEx$, where $q$ is charge per contour <length>. Integrating gives electric energy $-qEx^2/2$. Adding a constant entropic confinement <force> gives the displayed free-energy profile. Its interior maximum is at $x=f/(qE)$ and has height $f^2/(2qE)$; entry waiting and subsequent directed insertion are distinct times.
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