Cell membranes. Cell membranes (the walled enclosure around...

Cell membranes. Cell membranes (the walled enclosure around a cell) are typically about 7.5 nm thick. They are partially permeable to allow charged material to pass in and out, as needed. Equal but opposite charge densities build up on the inside and outside faces of such a membrane, and these charges prevent additional charges from passing through the cell wall. We can model a cell membrane as a parallel-plate capacitor, with the membrane itself containing proteins embedded in an organic material to give the membrane a dielectric constant of about $10 .$ (See Figure $18.52 . )$ (a) What is the capacitance per square centimeter of such a cell wall? (b) In its normal resting state, a cell has a potential difference of 85 $\mathrm{mV}$ across its membrane. What is the electric field inside this membrane?

Cell membranes. Cell membranes (the walled enclosure around a cell) are typically about 7.5 nm thick. They are partially permeable to allow charged material to pass in and out, as needed. Equal but opposite charge densities build up on the inside and outside faces of such a membrane, and these charges prevent additional charges from passing through the cell wall. We can model a cell membrane as a parallel-plate capacitor, with the membrane itself containing proteins embedded in an organic material to give the membrane a dielectric constant of about $10 .$ (See Figure $18.52 . )$ (a) What
is the capacitance per square centimeter of such a cell wall? (b) In its normal resting state, a cell has a potential difference of 85 $\mathrm{mV}$ across its membrane. What is the electric field inside this membrane?

Key Concepts

Capacitors

Capacitors are devices that store electrical energy in the form of an electric field between two conductive plates. Their performance is characterized by their capacitance, which depends on the area of the plates, the separation between them, and the properties of the material (dielectric) between the plates.

Dielectric Materials

Dielectric materials are insulators placed between the plates of a capacitor which increase its capacitance by reducing the effective electric field. This enhancement is quantified by the material’s dielectric constant, a measure of its ability to polarize in response to an electric field.

Parallel-Plate Capacitor Model

The parallel-plate capacitor model treats the capacitor as two large, flat, parallel conducting plates separated by a small distance. It simplifies the calculation of capacitance, with the capacitance per unit area given by the product of the permittivity (the product of the vacuum permittivity and the dielectric constant) divided by the separation distance.

Electric Field in Capacitors

The electric field in a capacitor is the force per unit charge within the space between the plates, and it can be determined by dividing the voltage difference by the separation distance. This concept is crucial for understanding how potential differences create uniform fields in ideal capacitor geometries.

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