Cell membranes (the walled enclosure around a cell) are typically about d = 8.0n

Question

Cell membranes (the walled enclosure around a cell) are typically about d = 8.0nm 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 70.

Part A

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

Express your answer using two significant figures.

Part B

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

Express your answer using two significant figures.

Explanation / Answer

a)

C/A = k*e0/d = 70*8.854*10^-12/8*10^-9 = 7.75*10^-6 F/cm^2 = 7.75 uF/cm^2

b)

E =V/d = 85*10^-3/8*10^-9 = 10.625*10^6 V/m = 10.625 MV/m

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