how to make current source for EM LF solvers?

I have a solid cylinder with dimensions & conductivity so chosen that it has a resistance of 5 Ohm; I also need to apply a current source of 1 A at 1 Hz. I expect a voltage drop of 5 V across the two ends of the cylinder. Furthermore, I expect the electric field inside the cylinder to be (almost) uniform and homogeneous, pointing from one end to the other. How should I go about doing this? For the purpose of my project, current source is preferred to voltage source. On paper, this is a simple electrostatic experiment but I cannot replicate it in S4L.
I have tried two solvers and they each returned unexpected results:
 Magneto QuasiStatic: A Ushape wire is used as current source, with two ends of the wire contacting two ends of the cylinder, thus making a close loop. Here, a voltage sensor is defined as an integration path between the two ends of the cylinder. Result: Voltage drop across the two ends is almost zero (order 10^9). Electric field is nonuniform and inhomogeneous. Magnetic field dominates the result.
 Electro QuasiStatic: Two circular electrodes are added at two ends of the cylinder, and they are assigned flux boundary condition; their value in A/m^2 is specified to give 1 A net current. The solver returns 0 for all field and voltage. The SolverLog says this is a trivial system with trivial solution.

The easiest way to achieve this in Sim4Life right now is to use the Electro Ohmic QuasiStatic solver, apply a voltage differential between the two ends of the cylinder, and compute the current flux at postprocessing. By virtue of the linearity of the equations, you can easily scale your results to a total flux of 1 A net current.