= Lateral stability of a spring-supported charge in a wedge
{title2=$T/\ell>q^2(\sqrt2+1/4)/(4\pi\epsilon_0y_e^3)$}
The electrostatic bisector <force> is laterally anti-restoring, with the positive stiffness coefficient on the right. A <spring> of tension $T$ and <length> $\ell$ adds transverse restoring stiffness $T/\ell$ when its fixed support is directly above the charge. The displayed inequality therefore distinguishes actual transverse stability from the saddle of a model with only a vertical <spring> <force>. Axial <spring> stiffness alone does not specify the transverse verdict. At fixed finite support geometry and positive gravitational load, sufficiently small <electric charge> preserves lateral stability: the destabilizing coefficient tends to zero as $q^2$, while the tension term approaches $mg/\ell>0$. The vertical <equilibrium> must separately satisfy its own positive-stiffness condition.
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