A cell membrane works as a capacitor. Muscle and nerve cells have excess negativ

Question

A cell membrane works as a capacitor. Muscle and nerve cells have excess negative charges inside that lead to a resting potential of -70mV inside the cell. A cell has a membrane with a thickness of 5.0nm and a capacitance of 90pF. a) what is the magnitude of the positive charge on the outside of the cell membrane, to the nearest pC? b) the sodium ions that help give rise to this potential are singly ionized Na+. What is the magnitude of the force on such an ion in the cell membrane, to the nearest pN?

Explanation / Answer

a) Q = CV

Q = (90 pF) (0.07 V) = 6.3 pC

b) E = V / d

V = 0.070 V and d = 5 x 10^-9 m

E = V/d = 1.4 x 10^7 N/C

F = qE = 1.6 x 10^-19 x 1.4 x 10^7

F = 2.24 x 10^-12 N = 2.24 pN

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