Force between similarly charged plates

[soothsayer]

In a setup I am designing, I have two conducting plates of similar charge, separated by 1mm of vacuum. The "top" plate, which is mechanically fixed, is charged to -10kV. The other "bottom" plate, which is electrically isolated, but not mechanically fixed (can move toward the "top plate"), is charged to -8kV. I am trying to determine what force the top plate exerts on the bottom plate.

Since both plates are highly negatively charged, I would expect the two to repel one another. However, since the top plate is more negatively charged than the bottom plate, it also seems like the top plate might induce a positive charge on the bottom plate and attract it, such as it would if the bottom plate were at 0kV.

I know how to calculate the force between two plates, assuming plates are infinite, and that they are oppositely charged, but I am getting confused by the like charges; how do I go about thinking about this problem?

Thanks for the help!

 

[Dale]

What you call 0 V is arbitrary. Only the 2 kV difference matters.

 

[jbriggs444]

In a setup I am designing, I have two conducting plates of similar charge, separated by 1mm of vacuum. The "top" plate, which is mechanically fixed, is charged to -10kV. The other "bottom" plate, which is electrically isolated, but not mechanically fixed (can move toward the "top plate"), is charged to -8kV. I am trying to determine what force the top plate exerts on the bottom plate.

To get past the concern expressed by @Dale, one might consider interpreting that "-10 kV" and that "-8 kV" as compared to a zero point at infinity. By definition, that would mean that a unit charge going from the -10kV plate to infinity would need to be given 10 kJoules of kinetic energy to make the trip. That would be a reasonable definition. But...

I know how to calculate the force between two plates, assuming plates are infinite,

If the plates are infinite and have a non-zero charge density, their potential is infinite. A test charge would experience a constant field gradient over an infinite distance. This means that it is impossible to have an infinite conductive plate at -10kV in any absolute sense.