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 = 0.15 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 = 5.

(a) Find the capacitance of the membrane.
____nF

(b) If the potential difference across the membrane is 88 mV, find the charge on each side of the membrane.
____nC

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

Explanation / Answer

Solution-

a) C = oA/d = 5*8.854x10^-12*2(10^-5*0.15)/10^-8

= 4.17x10^-8F

= 41.7 nF

b) q = C*v = 4.17x10^-8F*88x10^-3V

=3.67x10^-9C

= 3.67nC

c) E = V/d

= 88x10^-3/10^-8

= 8.8x10^6 V/m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.