A secretory cell's membrane has a hydrocarbon core of thickness and relative permittivity

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Biophysics & Medical Physics · Conductors, capacitance and boundary-value electrostatics

Life at Thermal Energy, Ch The membrane: barrier, capacitor and pump

Problem

A secretory cell's membrane has a hydrocarbon core of thickness d=3.0 nmd = 3.0\,\mathrm{nm} and relative permittivity εr=2.2\varepsilon_r = 2.2. Model the membrane as a parallel-plate capacitor with permittivity ε0εr\varepsilon_0\varepsilon_r and separation dd, using ε0=8.854×10−12 F m−1\varepsilon_0 = 8.854\times10^{-12}\,\mathrm{F\,m^{-1}}. ((a)) Find the membrane capacitance per unit area CmC_m, in μF cm−2\mathrm{\mu F\,cm^{-2}}. ((b)) Treating the whole surface of a spherical cell of radius 15 μm15\,\mathrm{\mu m} as having this CmC_m, find the total capacitance of the cell, in pF.

Browse the problem library