An unmyelinated axon with a radius of 0.9 μm and a length of 1.0 mm is in a salt solution at a temperature of 28 degrees Celsius. The ions in the solution distribute themselves uniformly in the region immediately surrounding the axon in response to positive ions (from protein residues) embedded in the membrane of the axon. Assume a 7.395×10^-1 nm^2 surface area per membrane-bound charge, and assume further that the charges are uniformly distributed and mobile. The membrane is in contact with an aqueous solution of NaCl at 28 degrees Celsius. The Debye length is 1.38 nm. Please solve clearly and explain briefly.
a) Calculate the areal charge density, σ (i.e. charge per unit surface area) of the membrane (in C/m^2).
b) Calculate the electric field at a distance of 2λDebye above the membrane (in N/C).
c) Calculate the electric field at a distance of λDebye/2 above the membrane (in N/C).
d) Calculate the concentration of salt needed to produce this Debye length of 1.38 nm (in mMol).