Chapter 8, Problem 54P

Some cell walls in the human body have a layer of negative charge on the inside surface. Suppose that the surface charge densities are $\pm 0.50\times {10}^{-3}C/m^2$ the cell wall is $5.0\times {10}^{-9}m$ thick, and the cell wall material has a dielectric constant of $\kappa$ = 5.4. (a) Find the magnitude of the electric field in the wall between two charge layers, (b) Find the potential difference between the inside and the outside of the cell. Which is at higher potential? (c) A typical cell in die human body has volume ${10}^{-16}{m}^3$ . Estimate the total electrical field energy stored in the wall of a cell of this size when assuming that the cell is spherical. (Hint: Calculate the volume of the cell wall.)