Field momentum inside a parallel plate capacitor

In summary, The conversation is discussing the concept of field momentum inside a cubic volume Omega, in relation to a system with a parallel plate capacitor where the top plate has a charge density of sigma and the bottom plate has a charge density of -sigma. The book referenced, Griffiths, is unclear on the concept of field momentum and suggests it is proportional to the Poynting vector ExB, leading to the conclusion that the field momentum is zero in this scenario. However, the problem later asks about a net flow of field momentum into the cubic volume Omega, which raises questions about the accuracy of the initial conclusion. The conversation concludes with the understanding that without a source of current or an AC circuit, the net flow of field momentum into volume
  • #1
brian0918
44
0
The system is a parallel plate capacitor, top plate has charge density sigma, bottom play has charge density -sigma. I'm looking for the "field momentum" inside the cubic volume Omega shown in the picture.

My book (Griffiths) is a little unclear on exactly what this is, and seems to be saying that the momentum is proportional to the Poynting vector ExB, so since there doesn't seem to be a magnetic field, this would suggest the field momentum is zero.

Is this correct?


The only problem I'm having is that, later in the problem, it asks if there's a net flow of field momentum into the cube, so I'm thinking there's more to the problem than what I'm seeing. Could anyone help clear this up?


Thanks.
 

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  • #2
Unless you have current flowing through the dielectric or it's part of an AC circuit you won't have a magnetic field. Is there any other information provided?
 
  • #3
There's no other information. So the field momentum is indeed zero?

What about a net flow of the field momentum into the cubic volume Omega?
 
  • #4
brian0918 said:
There's no other information. So the field momentum is indeed zero?

What about a net flow of the field momentum into the cubic volume Omega?

That would imply an infinite buildup of momentum/energy over time not to mention there is no source for that.
 
  • #5
Are you sure about the net flow into volume Omega being zero? If you look at the picture, the volume doesn't include the negative plate, just the positive plate. Does this change anything? The book doesn't explain this at all.
 

1. What is field momentum inside a parallel plate capacitor?

Field momentum inside a parallel plate capacitor refers to the movement or flow of electric charges between the two parallel plates. This momentum is created by the electric field that exists between the plates and is responsible for the storage of electrical energy in the capacitor.

2. How is field momentum related to the capacitance of a parallel plate capacitor?

Field momentum is directly proportional to the capacitance of a parallel plate capacitor. This means that as the field momentum increases, the capacitance also increases, and vice versa. This relationship is described by the equation C = εA/d, where C is the capacitance, ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates.

3. What factors affect the field momentum inside a parallel plate capacitor?

The field momentum inside a parallel plate capacitor is affected by several factors such as the distance between the plates, the surface area of the plates, and the dielectric material between the plates. Other factors that can affect the field momentum include the voltage applied to the plates and the type of material used for the plates.

4. How does the field momentum affect the energy stored in a parallel plate capacitor?

The field momentum inside a parallel plate capacitor is directly proportional to the energy stored in the capacitor. This means that the higher the field momentum, the more energy is stored in the capacitor. This relationship is described by the equation E = 1/2CV^2, where E is the energy stored, C is the capacitance, and V is the voltage applied to the plates.

5. How is the field momentum inside a parallel plate capacitor calculated?

The field momentum inside a parallel plate capacitor can be calculated using the equation p = εAd, where p is the field momentum, ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates. This equation can be derived from the capacitance equation, C = εA/d, by multiplying both sides by the voltage, V.

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