A typical biological cell has a volume of ${10}^{-9}c{m}^3,$ surface area of ${10}^{-6}c{m}^2,$ and a membrane thickness of ${10}^{-6}cm$; the dielectric constant of the membrane may be taken as $3($unitless$).$ Suppose that the concentration of $K^{+}$ions inside the cell is $0\mathrm{.}155M$ and that the Nernst potential across the cell wall is $0\mathrm{.}085V.$

a$.$ Calculate the net charge within the membrane, and

b$.$ Calculate the fraction of the $K^{+}$ions in the cell that are required to produce this charge.

Hint: vacuum permittivity, ${}_0=8\mathrm{.}852{10}^{-12}\frac{F}{m}$