Magnetic-to-electric energy ratio in a driven disc capacitor (${\overline{U}}_B/{\overline{U}}_E=(\omega a/c{)}^2/8$)

For thin parallel circular plates of radius $a$ and separation $L$, the quasistatic axial field $E_z(t)$ induces $H_{\varphi }={ϵ}_{0}r{\dot{E}}_z/2$. Integrating cycle-averaged vacuum energy densities for sinusoidal drive gives ${\overline{U}}_B/{\overline{U}}_E=(\omega a/c{)}^2/8$. The same fields have radial Poynting flux $S_r=-{ϵ}_{0}r{E}_z{\dot{E}}_z/2$, whose leading net inward power equals the time derivative of stored electric energy. The small ratio diagnoses the quasistatic regime.