= End-charged ideal polymer in an electric field
{title2=$\langle\mathbf R\rangle=Na^2q\mathbf E/(3k_BT)$}
An <ideal chain> with endpoint charges $+q$ and $-q$ has coupling energy $-q\mathbf E\cdot\mathbf R$ in a uniform <electric field>, when $\mathbf R$ points from negative to positive charge. Completing the square in its Gaussian end-to-end distribution gives the displayed mean extension. The force conjugate to end separation is $qE$, even though the two endpoints experience opposite forces; adding their magnitudes would double-count the work. The zero-field rms length is $a\sqrt N$, and the rms of a single Cartesian component is $a\sqrt{N/3}$. Direct endpoint interactions and charge-induced changes of solvent quality are excluded from this model.
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