Force on parallel plates at a given voltage

[physiker12]

Hello All,

I have noticed that a similar question have been asked many times here, but I still have doubts how to solve the parallel plates problem defined below:

Homework Statement

We have two freely moving parallel plates of area A, separated by distance d, one is grounded and the other is supplied with voltage from a regulated power supply which can also have its polarity reversed.
1. What is going to happen to the plates at a given voltage V?
2. What will happen to the plates when changing the voltage with constant speed dV/dt?
3. What will happen to the plates at voltage V when the polarity is suddenly changed?
4. How the problem will change when the plates are replaced with grids?

Homework Equations

See below.

The Attempt at a Solution

1. The plates will attract each other with force F(V,d) = V^2 * e_0 * A / (2 * d^2)
2. As above, but the equation gets more complicated and becomes a function of time. They should meet sooner than in #1.
3. Nothing should happen because of V^2, so sign doesn't play a role. Perhaps I'm underestimating some switching effects here?
4. Again, everything should be the same - to first approximation, ignoring the edge effects and fringe fields near the surface/edges.

Could anyone comment on my answers? Thanks.

 

[anathema]

Thank you for your question regarding the parallel plates problem. I would like to provide some insights and clarification on your answers.

1. Your answer for the first question is partially correct. The plates will indeed attract each other with a force given by F(V,d) = V^2 * e_0 * A / (2 * d^2). However, it is important to note that this force is only present when the voltage is applied to the plates. When the voltage is turned off, the plates will return to their neutral state and there will be no force between them.

2. Your answer for the second question is also partially correct. The equation for the force between the plates will indeed become more complicated and will depend on time as the voltage is changing. However, the plates will not necessarily meet sooner than in the first scenario. The speed at which they meet will depend on the rate of change of voltage, as well as other factors such as the distance between the plates and the material properties of the plates.

3. Your answer for the third question is incorrect. When the polarity of the voltage is suddenly changed, the force between the plates will also change. This is because the direction of the electric field between the plates will also change. This can have significant effects on the plates, such as causing them to vibrate or even break if the voltage change is large enough.

4. Your answer for the fourth question is generally correct. When the plates are replaced with grids, the problem becomes more complex due to the presence of multiple parallel conductors. In this case, the force between the plates will depend not only on the voltage and distance between them, but also on the geometry and arrangement of the grids.

I hope this helps to clarify your understanding of the parallel plates problem. If you have any further questions or concerns, please do not hesitate to ask.