A typical cell membrane in an animal maintains a potential difference across the membrane of ?V = 70 mV and the membrane has a thickness of about 8 nm. The capacitance of the membrane is about 1 microFarad per square cm.

(A) If we model the membrane by a simple "two thin sheets of charge" model separated by 8 nm with nothing between them, what would be the electric field be between the sheets and what would the charge density on the sheets of the membrane? Explain your reasoning.

(B) In order to maintain the potential difference across the two sides of the membrane, cells carry ions across a membrane against the field ("uphill") using a variety of active transport mechanisms. One mechanism does so by using up some of the cell's stored energy converting ATP to ADP. How much work does it take to carry one sodium ion (charge = +e) across the membrane against the field? Calculate your answer in eV/ion, Joules/ion, and kilcalories/mole (the last for 1 mole of sodium ions).