The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r
ID: 2180448 • Letter: T
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