Question

The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r = 10-5 m, length L = 0.32 m, and thickness d = 10-8 m. The membrane has a positive charge on one side and a negative charge on the other. Thus, it acts like a parallel-plate capacitor of area A = 2pirL and separation d. Its dielectric constant is kappa = 4. If the potential difference across the membrane is 74 mV, determine the magnitude of the charge on each side of the membrane.

Answer 1

Answer:

5.3 x 10⁻⁹ C

Explanation:

r = radius of cylindrical shell = 10⁻⁵ m

L = length = 0.32 m

A = area

Area is given as

A = 2πrL

A = 2 (3.14) (10⁻⁵) (0.32)

A = 20.096 x 10⁻⁶ m²

d = separation = 10⁻⁸ m

$k_{appa}$ = dielectric constant = 4

Capacitance is given as

$Q=\frac{k_{appa}\epsilon _{o}A}{d}$                               eq-1

V = Potential difference across the membrane = 74 mV = 0.074 Volts

Q = magnitude of charge on each side

Magnitude of charge on each side is given as

Q = CV

using eq-1

$Q=\frac{k_{appa} \epsilon _{o}AV}{d}$

Inserting the values

$Q=\frac{4 (8.85\times 10^{-12})(20.096\times 10^{-6})(0.074)}{10^{-8}}$

Q = 5.3 x 10⁻⁹ C