4. + , 13 points Tipler6 24. P.067. 0/6 Submissions Used My Notes Ask Your Teach

Question

4. + , 13 points Tipler6 24. P.067. 0/6 Submissions Used My Notes Ask Your Teacher The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r = 10-5 m, length L = 0.44 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/TrL 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 95 mV, find the charge on each side of the membrane. nC (c) Find the electric field through the membrane. V/m eBook

Explanation / Answer

(a)

The capacitance of a parallel-plate capacitor, filled with a dielectric of constant is

C = oA/d

C = [4*8.854x10-12*2(10-5*0.44)]/10-8

C = 9.786 x 10-8 F

C = 97.8 nF

(b)

The charge is given in terms of the capacitance and voltage as Q = C*v

Q = (9.786 x 10-8)*(95 x 10-3)

Q = 9.2968 x 10-9C

Q = 9.3 nC

c)

E = V/d

E = 95x10-3/10-8

E = 9.5 x 106 V/m

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