a. Find the capacitance of a circular piece of cell membrane that has a radius o

Question

a. Find the capacitance of a circular piece of cell membrane that has a radius of 4 m and is 8 nm across, and has a dielectric constant of 9.

b. The voltage difference between the inside the outside of that 8 nm wide cell membrane is 90 mV.

i. What is the magnitude of the electric field across the cell membrane?

ii. What is the force on a 3.82×10-26 kg sodium atom, which has a charge of q=+1.6×10-19 C?

iii. How quickly can it move across that membrane, if a clear channel opens up, and it accelerates from rest?

c. Calculate the total resistance of this circuit, and then calculate the current that is flowing from the battery and through each resistor. The battery provides 25V, and the resistances are R1=6, R2=7, and R3=8.

Explanation / Answer

r = 4um , d = 8 nm , k= 9

(a) C = Aeo*k/d

C = 3.14*(4*10^-6)^2*8.85*10^-12*9/(8*10^-9)

C = 0.5 pF

(b) V = 90 mV ,d = 8 nm

(i) E = V/d = 0.09/(8*10^-9)

E = 1.125*10^7 V/m

(ii) m = 3.82*10^-26 kg , q = 1.6*10^-19C

F = qE

F = 1.6*10^-19*1.125*10^7

F = 1.8*10^-12 N

(iii) F = ma

3.82*10^-26*a = 1.8*10^-12

a =4.7*10^-13 m/s^2

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