There was an interesting problem that appeared in POPTOR 2005: A generator consists of a parallel-plate capacitor immersed in a stream of conductive liquid with conductivity [tex]\sigma[/tex]. The surface area of a capacitor's plate is S, the distance between the plates is d. A liquid flows with constant velocity v parallel to the plates. The capacitor is in a uniform magnetic field B, which is perpendicular to the velocity and parallel to the plates. If the plates are connected to a resistor R, what is the current that flows through the resistor? I understand that the free charges inside the conductive liquid will feel a magnetic force, and thus begin "build up" on the plates. "Build up" is in quotation marks because I think that the charges are still moving with the liquid flow, but are right up against the plates. This will continue until an electrostatic field is established that perfectly cancels out the magnetic forces acting on the free charges in the moving fluids. Thus the voltage of the capacitor by itself would be vBd. I would then divide that voltage by R to get the current through the resistor. However, the solution that POPTOR gives is that the capacitor is in series with both R and the "internal resistance" of the fluid. Why does the resistance of the fluid matter? The voltage between the two plates is vBd regardless of the fluid inside.