Opening of voltage-gated channels is driven by an intramembrane electric field acting on charged voltage-sensor domains. These domains move across the membrane and generate gating (displacement) currents. When these currents are integrated over time, they produce the gating charge generated by a population of channels. What would be the gating charge passing through the external circuit when the flat array of charges moves across the distance a inside the membrane? The hydrophobic thickness of the membrane is d, the dielectric constant ɛ, the density of charges is O and the area of the membrane is A (provide an analytic solution).

Opening of voltage-gated channels is driven by an intramembrane electric field acting on charged voltage-sensor domains. These domains move across the membrane and generate gating (displacement) currents. When these currents are integrated over time, they produce the gating charge generated by a population of channels. What would be the gating charge passing through the external circuit when the flat array of charges moves across the distance a inside the membrane? The hydrophobic thickness of the membrane is d, the dielectric constant ɛ, the density of charges is O and the area of the membrane is A (provide an analytic solution).