Abstract
The spatial dependence of electric potential inside a spherical shell of charge in the presence of mobile ions is examined. It is shown that isopotentiality inside the sphere is a possible solution to the Poisson-Boltzmann equation, but the conditions required for this solution are not satisfied in the case of biological cells. It is then shown how diffuse double layer considerations affect the form of the Goldman equation for membrane potential. It is shown that an equation essentially identical in form with the Goldman equation results in each of the three cases: no diffuse double layers (neutral membrane), diffuse double layer on one side only, and diffuse double layers on both sides of the membrane. Membrane potential theory and measurement are discussed.
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