Circular bending energy of an elastic filament
= Circular bending energy of an elastic filament
{title2=$E=\pi K_b/R$}
A circular loop of <radius> $R$ has constant curvature $1/R$ and contour <length> $2\pi R$. Integrating the quadratic bending <energy> <density> $K_b/(2R^2)$ gives the displayed <energy>. With $K_b=k_BTA$ this is $\pi k_BTA/R$. Applied-force work, axial <strain>, twist and contact energies are separate terms; the loop formula alone does not determine an actual loaded loop's <radius>.