The membrane surrounding a living cell consists of an inner and an outer wall th

Question

The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. Assume that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 7.0 × 10-6 C/m2. (a) What is the magnitude of the electric field within the cell membrane? (b) Find the magnitude of the electric force that would be exerted on a potassium ion (K+; charge = +e) placed inside the membrane.

Explanation / Answer

A) Capacitance C = Q/V = Q/(E*d) = eo*A/d

eo = permittivity of free space = 8.85*10^-12 C^2/(N.m^2)

then C = Q/E = eo*A

then electric field E = Q/(eo*A) = (1/8.85*10^-12)*(7*10^-6) = 7.909*10^5 N/C or V/m

B) Force F = q*E = 1.6*10^-19*7.909*10^5 = 12.655*10^-14 N

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