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 = 0.14 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?rL and separation d. Its dielectric constant is about ? = 5.
(a) Find the capacitance of the membrane.

_____ nF

(b) If the potential difference across the membrane is 89 mV, find the charge on each side of the membrane.

_____ nC

(c) Find the electric field through the membrane.

______V/m

Explanation / Answer

a)C=A/d=AK0/d=2rLK0/d

=2*3.14*10^-5*0.14*5*8.89*10^-12/10^-8

=39.04*10^-9=39.04nF

b)Q=CV=39.04*10^-9*89*10^-3=3.478*10^-9=3.478nC

c)E=Vd=89*10^-3/10^-8=89*10^5V/m

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