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 = 0.21 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 = 2prL 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 50 mV, find the charge on each side of the membrane. (nC)

(c) Find the electric field through the membrane. (V/m)

Explanation / Answer

C = ??oA/d = 3*8.854x10^-12*2?(10^-5*0.25)/10^-8 = 4.17x10^-8F = 41.7 nF

b) q = C*v = 4.17x10^-8F*79x10^-3V =3.30x10^-9C = 3.30nC

c) E = V/d = 79x10^-3/10^-8 = 7.9x10^6 V/m

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