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.

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

= dielectric constant = 4

Capacitance is given as

                              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

Inserting the values

Q = 5.3 x 10⁻⁹ C

inverse v=i*r

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