# Force between similarly charged plates

• soothsayer
In summary: I am getting confused by the like charges; how do I go about thinking about this problem?Perhaps one way to approach this problem is to think about the fields surrounding the plates. Recall that each plate is negatively charged, so the fields would be in opposite directions. If the top plate were to move closer to the bottom plate, the fields would increase in intensity because the charge on the bottom plate would be cancelled out by the field from the top plate. However, if the bottom plate were to move closer to the top plate, the fields would decrease in intensity because there would be more positive charge on the top plate than on the bottom plate. This difference in field intensity would cause a
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!

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

soothsayer said:
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.

Dale

## 1. What is the force between similarly charged plates?

The force between similarly charged plates is the electrostatic force of repulsion between two plates that carry the same type of charge. This force is caused by the interaction of the electric fields produced by the charges on the plates.

## 2. How is the force between similarly charged plates calculated?

The force between similarly charged plates can be calculated using Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

## 3. What factors affect the force between similarly charged plates?

The force between similarly charged plates is affected by the magnitude of the charges on the plates, the distance between the plates, and the dielectric constant of the material between the plates. It is also affected by the presence of any other nearby charges or external electric fields.

## 4. Can the force between similarly charged plates be attractive?

No, the force between similarly charged plates is always repulsive. This is because similarly charged particles have the same type of charge and therefore repel each other.

## 5. How does the force between similarly charged plates affect the movement of charged particles?

The force between similarly charged plates can affect the movement of charged particles by either attracting or repelling them. If the plates are positively charged, they will repel positively charged particles and attract negatively charged particles. This can cause charged particles to move towards or away from the plates, depending on their charge.

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