The membrane of the axon of a nerve cell is a thin cylindric

The membrane of the axon of a nerve cell is a thin cylindrical shell of radius r = 10-5 m, length L = 0.09 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 = 7. If the potential difference across the membrane is 60 mV, determine the magnitude of the charge on each side of the membrane.

Solution

C = dielectric constant * r L / 2kd

= (7 * 10^-5 * 0.09) / (2 * 8.99 * 10⁹ * 10^-8)

= 3.5 * 10^-8 F

Q = C V = 3.5 * 10^-8 * 60 * 10^-3

= 2.1 * 10-9 C

= 2.1 nC