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 = 0.12 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 = 2rL and separation d. Its dielectric constant is about = 6.

(a) Find the capacitance of the membrane.
____ nF

(b) If the potential difference across the membrane is 35 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 = oA/d

        = 6*8.854x10^-12*2(10^-5*0.12)/10^-8 = 4.00x10^-8F = 40.0 nF

(b) q = C*v = 4.00x10^-8F*35x10^-3 V = 1.40 x 10^-9 C = 1.40 nC

(c) E = V/d = 35x10^-3/10^-8 = 3.5 x 10^6 V/m

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