Chapter 24, Problem 24.38E

BIO Potential in Human Cells. 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 5.0 nm thick, and the cell-wall material is air. (a) Find the magnitude of $\stackrel{\to }{\text{E}}$ in the wall between the two layers of charge, (b) Find the potential difference between the inside and the outside of the cell. Which is at the higher potential? (c) A typical cell in the human body has a volume of 10⁻¹⁶ m³. 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.) (d) In reality, the cell wall is made up, not of air, but of tissue with a dielectric constant of 5.4. Repeat parts (a) and (b) in this case.