Cell membranes (the walled enclosure around a cell) are typically about d = 7.6

Question

Cell membranes (the walled enclosure around a cell) are typically about d = 7.6 nm thick. They are partially permeable to allow charged material to pass m 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 41. (See the figure 1). What is the capacitance per square centimeter of such a cell wall? Express your answer using two significant figures. In its normal resting state, a cell has a potential difference of 85 m V across its membrane. What is the electric field inside this membrane? Express your answer using two significant figures.

Explanation / Answer

Capacitance, C = koA/d.
o is the vacuum permittivity, o = 8.85 x 10-12 F/m
k is the dielectric constant, k = 41.
d = 7.6 nm = 7.6 x 10-9 m.
A = 1 cm2. = 10-4 m2
C = [41 x (8.85 x 10-12) x (10-4)] / (7.6 x 10-9) = 4.77 x 10-6 F.

b)
V = 85 mV = 85 x 10-3 V
E = V/d = (85 x 10-3) / (7.6 x 10-9) = 11.18 x 106 V/m

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