Problem 18.59: Cell membranes. Cell membranes (the walled enclosure around a cel

Question

Problem 18.59: Cell membranes.

Cell membranes (the walled enclosure around a cell) are typically about d = 8.0 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 63. (See the figure(Figure 1) .)

Part A

What is the capacitance per square centimeter of such a cell wall?

Express your answer using two significant figures.

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Part B

In its normal resting state, a cell has a potential difference of 85 mV across its membrane. What is the electric field inside this membrane?

Problem 18.59: Cell membranes.

Cell membranes (the walled enclosure around a cell) are typically about d = 8.0 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 63. (See the figure(Figure 1) .)

Part A

What is the capacitance per square centimeter of such a cell wall?

Express your answer using two significant figures.

c =   F/cm2  

SubmitMy AnswersGive Up

Part B

In its normal resting state, a cell has a potential difference of 85 mV across its membrane. What is the electric field inside this membrane?

Express your answer using two significant figures.

Outside axon Axon membrane Inside axon

Explanation / Answer

part a)

d = 8 nm

k = 63

part a)

capacitance per square centimete = epsilon * Area/d

capacitance per square centimete = 8.854 *10^-12 * 1 *10^-4/(8 *10^-9)

capacitance per square centimete = 1.11 *10^-7 F/cm^2

part B)

for the electric field

electric field = V/d

electric field = 85 *10^-3/(d)

electric field = 85 *10^-3/(8 *10^-9)

electric field = 1.063 *10^7 V/m

the electric field inside the membrane is 1.063 *10^7 V/m

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