The membrane of the axon of a nerve cell is a thin cylindricalshell of radius r = 10-5 m, length L = 0.09 m, and thickness d = 10-8 m. The membrane has a positive chargeon one side and a negative charge on the other, and acts as aparallel-plate capacitor of area A =2πrL and separation d. Its dielectricconstant is about κ = 7.
a) Find the capacitance of the membrane.
b) If the potential difference across the membrane is 45 mV, find the charge on each side of the membrane.
c) Find the electric field through the membrane.