LF Electro Ohmic Quasi-Stat. gives unexpected current density

[Cindy645]

Hi all! I use the following very simple structure to test whether I am using the LF Ohmic Quasi-Static Solver correctly. The voltage comes out as expected but the current (density) is incorrect. I have these three electrodes of the same radius (1mm) stacking together (touching each other) in an electrode-cylinder-electrode configuration. I want to apply to a 2V (+1V top, -1V bottom) to the two silver electrodes and achieve a 1 kA current through. So I chose the cylinder material (copper) and length such that the resistance is 2 mOhm.

After running the simulation, where I place a line as voltage sensor (it runs from 2mm offset from the top electrode to 2mm offset from the bottom electrode, in the centre), it gives a value of -1.9786V as expected.
When I combine the J(x,y,z,f0) from the overall field and a plane I created and use flux evaluator to measure total current density as described here https://forum.zmt.swiss/topic/24/compute-the-total-current-flowing-between-two-electrodes-in-an-electro-quasistatic-lf-simulation, unexpected resutls occur. I tried two different planes and they gave different results::

1. A block with 0mm thickness and 1m x 1m in area in the middle of the cylinder parallel to the electrodes, result: 1 A/m^2, multiply by the area gives 1A
2. A cylinder with 0mm thickness and 1mm in radius in the middle of the cylinder parallel to the elctrodes, resutls: 49.7369 A/m^2, multiply by the area gives 0.156mA
   (P.S. why the current density has a unit of [A/m^2 m^2]?)

Model, Simulation and Analysis details are summaried in the screenshots attached.