8.5.P3

We have discussed the motion of electrons in a conductor and the conditions under which Ohm’s law arises in a resistor. But there are other situations in which potential differences lead to current flow. Consider a simple model of current flow in a liquid: a tube of fluid containing (equal amounts of) positive and negative ions with membranes on each end. The membranes are kept at (different) uniform potentials and that allow the ions to pass through them. (We assume that there are sources of ions on the other side of the membranes so that the density of ions in the tube can remain constant.) The ions can move through the fluid, but they feel a drag force, F_drag = -bv. The positive and negative ions are both singly charged, but they are of different sizes, so they have different drag coefficients. The negative ions have a larger drag coefficient. Since the fluid is neutral, there will be the same of positive and negative ions per unit volume of the fluid.

Suppose that as a result of the potential difference on the two membranes, there is an E field pointing to the left.

1. At steady state, which ions move faster, + or -, or do they go with the same speed?
2. Do you expect there to be a net current? If so, in which direction is it? Explain your reasoning.

Joe Redish 5/21/12