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 6.9 × 10-6 C m a what is the magnitude of the electric fleld 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. (a) Number Units Units (b) Number

Explanation / Answer

given

effective charge density, sigma = 6.9*10^-6 C/m^2

a. cell membrane thickness, t = 4 nm ( from google)

average cell diameter, d = 100 um

capacitance of the cell = C

C = 1/k(1/(d/2 - t) - 2/d) = 1/8.98*10^9*(1/(50um - 4nm) - 2/100um) = 6.959*10^-11 F

Q = CV

V = Q/C

and

Q = sigma*pi*d^2

V = 0.003114799 V

hence

electric field = E

E = V/t = 778699.751987 V/m

also

sigma = 6.9*10^-6

as the plates are close we can coisdier the region to have constant leectric field due to infinite plates

hence

E = sigma/epsilon = 4*pi*sigma*k = 778637.456 V/m

b. force = qE = 1.6*10^-19*E = 1.245*10^-13 N

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