8.3.P8
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A biology researcher wants to study the electrical properties of a few square micrometers of membrane. The thickness of the membrane is a few nanometers. He decides that he will mentally model this bit of the membrane as if it were a flat pair of infinite sheets of (infinitely thin and smooth) charge with charge density σ Coulombs/μm2.
A. In his first draft of the model, he visualizes the membrane as filled with empty space. A coordinate system is shown with the origin right at the center of the membrane. Draw graphs of what the x and y components of the electric field and the electrostatic potential along the x-axis would look like in this model. Be careful about the shape and be sure to show what would happen outside the plates, both to the left and right.
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Explain why you have drawn the graphs the way you have.
B. To improve the model, he imagines that the region between the sheets of charge is filled with a uniform dielectric of dielectric constant, κ = 7. How would the graphs you have drawn in part A change?
C. Given that you want to charge the membrane to the same charge density in both cases, would the energy needed to charge the model membrane be more with empty space or with a dielectric filling the space between the charged sheets? Explain your reasoning.
D. Is this a reasonable starting point for a model of a membrane or not? Why do you think so?
Joe Redish 3/5/12
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