The human nerve cell is composed of axons, which are the primary transmission li

Question

The human nerve cell is composed of axons, which are the primary transmission lines of the nervous system, and as filamentary bundles they form nerves. Some axons can extend up to one meter or more while others extend as little as one millimeter. the longest axons in the human body arc those of the sciatic nerve, which run from the base of the spinal cord to the big toe of each foot. A potential difference of-89 mV exists due the flow of positively charged K + ions into, and out of the cell's membrane though openings in the axon's membrane, called ion channels. The positively charged folded proteins in the cell interior cannot be transported though the narrow ion channels, and it is this charge imbalance which gives rise to the observed potential difference across the thin cell membrane. Treating the membrane walls as a parallel plate capacitor, with no dielectric, calculate the effective capacitance of the axon cell membrane. In addition, calculate- the magnitude of the electric field across the membrane. Choose from one of the answers shown below.

Explanation / Answer

V = 89 mV = 89 x 10^-3 V

d = 7.5nm = 7.5 x 10^-9 m

V = E.d

E = 89 x 10^-3 / ( 7.5 x 10^-9) = 11.9 x 10^6 V/m

For parrallel plate capacitor

C = A e0 / d

C / A = e0 / d = 8.854 x 10^-12 / 7.5 x 10^-9   = 1.2 x 10^-3 F /m^2

      = 1.2 x 10^-3 x 10^-4 F / cm^2   = 0.12 x 10^-6 F / cm^2 = 0.12 uF / cm^2

Ans (C)

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