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/m2, the cell wall is 5.1 nm thick, and the cell-wall material is air.

Notes about Problem 18.77 and a Hint for Part D: The cell wall/membrane creates a separation of charge between the inside and outside of a cell and thus acts as a capacitor! (I have used this fact as motivation for exam problems in the past...) The "total electric field energy" is the energy stored in the capacitor. To find this, we need to first determine the capacitance. The "plate area" is given by A = 4*pi*r^2, where r is determined from the given volume. To save you the headache of this geometry, the result is A = 1.042*10^-10 m^2. The capacitance can be found using the parallel plate capacitor equation, using the area given as the plate area and the thickness of the cell wall as the plate separation d. Once you have the capacitance, use the known value of the charge on your "capacitor" to find the energy!

A. Find the magnitude of E⃗ in the wall between the two layers of charge. Express your answer using two significant figures.

B. Find the potential difference between the inside and the outside of the cell. Express your answer using two significant figures.

C. Which wall of the cell is at the higher potential? (Inner or outer wall)

D. A typical cell in the human body has a volume of 10−16m3 . 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.) Express your answer using two significant figures.

E. In reality, the cell wall is made up, not of air, but of tissue with a dielectric constant of 5.4. Repeat part A in this case. Express your answer using two significant figures.

F. In reality, the cell wall is made up, not of air, but of tissue with a dielectric constant of 5.4. Repeat part B in this case. Express your answer using two significant figures.

Answer 1

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