Force between parallel plates of set voltage

In summary, the conversation discusses the calculation of electrostatic force between two parallel plates with different voltages. The formula for force is derived from the energy stored in a capacitor, and the voltage difference between the plates is the key factor. The common mode voltage does not affect the calculation.
  • #1
soothsayer
423
5
Hi PF,

I have a setup with two plates that are connected to two different voltages and separated by vacuum. In my case, one plate is set at -10kV, and the other plate is set at -7.5kV. I know the area of these plates, the separation of the plates (which is much smaller than the plate area), and the voltage difference between the two plates (2.5kV) and I am trying to set up a way of calculating what the electrostatic force between these plates would be under these conditions, but I am having trouble conceptualizing the problem.

I am used to thinking about this problem in terms of capacitors, where a voltage is applied across the parallel plate capacitor and each plate is imparted with opposite charges ±Q. In that situation, I know I can calculate the force between the plates using the following equation:

F = ε0 AV2 / 2d2

But I don't know if this equation still holds in my situation, where I have two parallel plates in space, each connected to a different voltage. Can I just insert the 2.5kV voltage difference between my plates into the equation above for V and get an accurate result? I tried it and got a reasonable result but don't exactly trust it.

Thanks for the help.
 
Physics news on Phys.org
  • #2
Yes, what you have done should be correct. The common mode voltage doesn't make any difference, it is the voltage difference that causes the force. It's easy to come up with the formula you quoted. The energy stored in the capacitor is [itex] E = \frac{C V^2}{2} = \frac{\epsilon_0 A v^2}{2 x}[/itex], where x is the plate separation. The force will just be [itex]-\frac{dE}{dx} = \frac{\epsilon_0 A V^2}{2 x^2}[/itex].
 
  • Like
Likes sophiecentaur and CWatters
  • #3
Thanks, phyzguy!
 
  • #4
Only the voltage difference matters, not the absolute voltages.
 
  • Like
Likes sophiecentaur

What is the force between parallel plates of set voltage?

The force between parallel plates of set voltage, also known as the electrostatic force, is the attraction or repulsion between two charged plates that are parallel to each other and have a constant voltage difference between them. This force is caused by the electric field that is created between the plates due to the difference in potential energy.

How is the force between parallel plates of set voltage calculated?

The force between parallel plates of set voltage can be calculated using the formula F = QE, where F is the force in Newtons, Q is the charge on the plates in Coulombs, and E is the electric field strength in Newtons per Coulomb. This formula assumes that the plates are infinitely large and parallel, and that the electric field is uniform between the plates.

What factors affect the force between parallel plates of set voltage?

The force between parallel plates of set voltage is affected by several factors, including the distance between the plates, the voltage difference between the plates, and the magnitude and direction of the charges on the plates. Additionally, the presence of any other electrically charged objects in the vicinity can also affect the force between the plates.

What is the direction of the force between parallel plates of set voltage?

The direction of the force between parallel plates of set voltage depends on the charges on the plates. If the plates have the same charge, they will repel each other, and the force will be directed away from the plates. If the plates have opposite charges, they will attract each other, and the force will be directed towards the plates.

What are some real-world applications of the force between parallel plates of set voltage?

The force between parallel plates of set voltage has many practical applications, such as in capacitors, which use this force to store electric charge. It is also used in devices like deflection plates in cathode ray tubes, inkjet printers, and photocopiers. Additionally, the force between parallel plates is essential in understanding the behavior of charged particles in electric fields, which has applications in fields like particle accelerators and plasma physics.

Similar threads

  • Electromagnetism
Replies
18
Views
1K
Replies
9
Views
1K
Replies
7
Views
1K
Replies
8
Views
2K
Replies
61
Views
2K
Replies
7
Views
17K
Replies
8
Views
1K
Replies
1
Views
1K
Replies
2
Views
2K
Replies
12
Views
2K
Back
Top