The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r
ID: 1374752 • 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 = 0.49 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 ? = 4.
The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r = 10^-5 m, length L = 0.49 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 = 2pirL and separation d. Its dielectric constant is about k = 4. (a) Find the capacitance of the membrane. nF (b) If the potential difference across the membrane is 52 mV, find the charge on each side of the membrane. nC (c) Find the electric field through the membrane. V/mExplanation / Answer
a)
The capacitance of the memebrane is
C = e_o A / d
= e_o ( 2 pi r L ) / d
= ( 8.85*10^ -12 ) 2 pi (10^-5 m ) (0.49 m ) / 10^ -8 m
=2.72*10^ -8 F
= 27.2 nF
b)
Charge on each side of memebrane is
Q = C V
= (27.2 nF) (52 mV)
= 1.414 nC
c)
Electric field through membrane is
E = V / d
= 52 *10^ -3 V / ( 10^ -8 m )
=52 *10^ 5 V / m
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