Some cell walls in the human body have a layer of negative charge on the inside

Question

Some cell walls in the human body have a layer of negative charge on the inside surface and a layer of positive charge of equal magnitude on the outside surface. Suppose that the charge density on either surface is ± 0.50×10^3 C/m^2, the cell wall is 5.00 nm thick, and the cell-wall material is air. I've done the first two question but I'm having trouble with the last 3 please help!!

A) Find the magnitude of E in the wall between the two layers of charge. Answer is 5.65*10^7 V/m

B) Find the potential difference between the inside and the outside of the cell. Which is at the higher potential? The answer is 0.282 V.

C) A typical cell in the human body has a volume of 10^16 m^3 . Estimate the total electric-field energy stored in the wall of a cell of this size. (Hint: Assume that the cell is spherical, and calculate the volume of the cell wall.) U=???J

D) In reality, the cell wall is made up, not of air, but of tissue with a dielectric constant of 5.40. Repeat part A in this case. E=??? V/m

E) In reality, the cell wall is made up, not of air, but of tissue with a dielectric constant of 5.40. Repeat part B in this case. deltaV=???V

Explanation / Answer

b) if we assume it as a parallel plate capacitor then

C = e0*A / d

and Q = CV

V = Q/C = Q / (e0*A / d ) = (Q/A) (d/e0)

V = (0.50 x 10^-3) ( (5 x 10^-9) / (8.854 x 10^-12))

V = 0.282 volt

a) E = V/d = 0.282 / (5 x 10^-9) = 5.65 x 10^7 V/m

c) energy stored = QV/2

volume = area x d

area = (10^-16) / (5 x 10^-9) = 2 x 10^-8 m^2

charge Q = (0.50 x 10^-3 ) x (2 x 10^-8) = 1 x 10^-11 C

energy = (1 x 10^-11 x 10^-16) / 2 = 5 x 10^-28 J

E) C ' = kC = 5.40C

then V = Q / C' = Q / 5.40C = 0.282 / 5.40 = 0.0522 V

d) E = V/d = 5.65 x 10^7 / 5.40 = 1.05 x 10^7 V/m

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