The membrane of the axon of a nerve cell can be modeled as a thin cylindrical sh

Question

The membrane of the axon of a nerve cell can be modeled as a thin cylindrical shell of radius 1.00 times 105 m. having a length of 10.0 cm and a thickness of 10.0 inn. The membrane has a positive charge on one side and a negative charge on the other, and the membrane acts as a parallel-plate capacitor of area 2pirL and separation d. Assume the membrane is filled with a material whose dielectric constant is 3.00. Find the capacitance of the membrane. If the potential difference across the membrane is 70.0 mV. find the charge on the positively charged side of t he membrane.

Explanation / Answer

Given Radius of the shell is , r = 1.00 *10^5 m Length of the shell is , L = 0.1 m Thickness of the shell is , t = 10.0 nm Value of dielectric constant is , k = 3.0 The seperation between the plates is d Area of the capacitor is 2rL = 2 *3.14 *(1.00 *10^5 m) *0.1 m A = 62800 m^2 1) The capacitance of the membrane is C = koA/d                     C = 3.0 *(8.85 *10^-12F/m) *62800 m^2 /d                         = (1.6*10^-6 /d) F 2) The potentail difference is , V = 70 mV the charge q = CV = (1.6*10^-6 /d) F * 70mV                    q = (1.16*10^-7/d) C

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