A cell membrane acts as a parallel-plate capacitor with a spacing of 13 nm and filled with water. Suppose the positive plate is on top, and the negative plate is on the bottom, and the electric field is 40 N/C. A sodium ion with an excess charge of +e passes through the membrane at an initial speed of .03 m/s.
a) Draw the directions of electric field and force acting on the sodium ion. What is the magnitude of the net force?
b) Does it gain or lose electrostatic potential energy? How would this answer be different if the ion were negative?
c) What is its final speed? (Neglect the effects of gravity)
d) What is the capacitance of the membrane?
e) What would the electric field inside the membrane be if it consisted of free space instead of water? Would the new field allow the cell membrane to retain more charge or less, compared to water?