= Steady fields in two leaky dielectric layers
{title2=$\sigma_1E_1=\sigma_2E_2$}
For two planar homogeneous layers in series, <charge conservation> makes the steady normal <current density> the same in both layers. Combining <Ohm's law> with $E_1d_1+E_2d_2=V$ determines the fields when both conductivities are positive. The free interfacial <surface charge density> is $\epsilon_2E_2-\epsilon_1E_1$, whereas total free-plus-bound charge is $\epsilon_0(E_2-E_1)$. The two notions of charge are distinct. This DC state can differ from the immediate response to switching the voltage; interfacial free charge accumulates during the transient.
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