Question
Asked Sep 25, 2019

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) 

(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 mV across its membrane.  What is the electric field inside this membrane?

(HINT:  Don’t forget to multiply by the given dielectric constant.)

7.5 nm
Outside axon
+
Axon membrane
Inside axon
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7.5 nm Outside axon + Axon membrane Inside axon

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Expert Answer

Step 1

The thickness of the membrane is 7.5nm, and dielectric constant is about 10.

(a) Write the expression for the capacitance between parallel plates.

 

here, A is the area of cross section
d is the distance between plates
E is the dielectric constant of free space
k is the dielectric constant of material
kegA
C =
d
C_10x 8.85 x 1012 F/m
7.5x 109 m
A
1.18x 10 F/cm2
1.18F/cm
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here, A is the area of cross section d is the distance between plates E is the dielectric constant of free space k is the dielectric constant of material kegA C = d C_10x 8.85 x 1012 F/m 7.5x 109 m A 1.18x 10 F/cm2 1.18F/cm

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Step 2

(b) Write the expression for electric...

[V is the potential
substitute 85x 103v for V
V
E=
d
85x 103 V
7.5x10
m
- 11.3x 10 V/m
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[V is the potential substitute 85x 103v for V V E= d 85x 103 V 7.5x10 m - 11.3x 10 V/m

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