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 m, length L 0.48 m, and thickness d 108 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 2arL and separation d. Its dielectric constant is about 7.

Tipler6 24,P.067. 1 2 3 The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r 10 5 m, length L-0.48 m, and thickness d. 108 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 rt and separation d. Its dielectric constant is about K-7. 1) (a) Find the capacitance of the membrane. 163 You currently have 4 submissions for this question. Only 10 submission are allowed. You can make 6 more submissions for this question. (b) If the potential difference across the membrane is 97 mV, find the charge on each side of the membrane. 3721 nc submit You currently have 1 submissions for this question only 10 submission are allowed. You can make 9 more submissions for this question. (c) Find the electric field through the membrane. Vim Submit You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Tipler6 24. P.062. Tipler6 24. 067 Tipler6 24. P.088 Tipler6 25. P.004 Tipler 6 25. P.034.

Explanation / Answer

1)

C= k Eo A /d

where k= dielectric constant

Eo=permittivity of free space

A = area

d= distance between plates

k=7

Eo=8.854e-12 F/m

A=2 X pi X r X L=3.0159e-5 m2

d=E-8 m

C= 1.869e-7 F

=186.9 nF

2)

V= Ed=q X d / (k Eo A)

Where E= electric field

from above equation q= V k Eo A /d=(97e-3 X 7 x 8.854e-12 x 3.0159e-5)/e-8 (these e denote 10 ^ )

18.131nC

3)E= V/d=97e-3/e-8=9.7e6 V/m=9700000 V/m

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