The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r

Question

The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r = 10^-5 m, length L = 0.35 m, and thickness d = 10^-8 m. The membrane has a positive charge on one side and a negative charge on the other, and acts as a parallel-plate capacitor of area A = 2 pi*r*L and separation d. Its dielectric constant is kappa = 8

(a) Find the capacitance of the membrane? ______ nF

If the potential difference across the membrane is 71 mV, find
(b) the charge on each side of the membrane _______ nC

(c) the electric field through the membrane _______ V/m

Explanation / Answer

a)

C = k e0 A/d = 8*8.85e-12*2*3.1416*1e-5*0.35/1e-8 = 155.7 = 156 nF

b)

Q = CV = 155.7*71e-3 = 11.1 nC

c)

E = V/d = 71e-3/1e-8 = 7100000 V/m

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