Force acting on a dielectric placed between parallel plates

In summary, we have a parallel plate capacitor with length l, width w, and separation d, and a dielectric of dielectric constant k inserted to a distance x. With a constant charge q, we can find the force acting on the dielectric by calculating the effective capacitance as εw(kx+l-x)÷d and the energy stored as q^2d÷(2εw(kx+l-x)). By differentiating the energy with respect to distance, we get a force of q^2d(k-1)÷(2εwl^2) in the length direction.
  • #1
carlyn medona

Homework Statement


A parallel plate capacitor of length l and width w and separation d, has a dielectric of dielectric constant k inserted to a distance x, if the capacitor has a charge q, find force acting on the dielectric when its near the edge

Homework Equations

The Attempt at a Solution

. [/B]
I found effective capacitance which was εw(kx+l-x)÷d and found force to be equal to q^2 d(k-1)÷(2εwl^2) is this right?
 
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  • #2
carlyn medona said:
inserted to a distance x
inserted how? From which direction?
carlyn medona said:
if the capacitor has a charge q
Before or after the dielectric is inserted?
carlyn medona said:
I found effective capacitance which was εw(kx+l-x)÷d and found force to be equal to q^2 d(k-1)÷(2εwl^2)
Can you please show your detailed calculation? And a diagram would be helpful as well. Thanks.
 
  • #3
carlyn medona said:
q^2 d(k-1)÷(2εwl^2)
Assuming the insertion is in the length direction, that looks right to me.
 
  • #4
It was inserted from top, can't get the diagram, and there is no external power source so I expect q to be a constant, so I found capacitance εw(kx-x+l)÷d and energy stored q^2d÷(2εw(kx+l-x) so I found force by differentiating energy with respect to distance and got. q^2d(k-1)÷(2εwl^2)
 
  • #5
carlyn medona said:
It was inserted from top
But is that the "length" direction or the "width" direction? Judging from your reference to l-x it is the length direction.
carlyn medona said:
found force by differentiating energy with respect to distance
That's the method I used, getting the same result.
 
  • #6
Length direction, and thanks for confirming
 

1. What is a dielectric?

A dielectric is a material that does not conduct electricity, but can become polarized when placed in an electric field.

2. How does a dielectric affect the force between parallel plates?

A dielectric placed between parallel plates will experience a force due to the electric field created by the plates. This force is known as the dielectric force and is caused by the polarization of the dielectric material.

3. How does the dielectric constant affect the force on a dielectric?

The dielectric constant, also known as the relative permittivity, is a measure of how easily a material can be polarized. A higher dielectric constant means that the material can be more easily polarized, resulting in a stronger dielectric force.

4. Does the distance between the parallel plates affect the force on a dielectric?

Yes, the force on a dielectric placed between parallel plates is inversely proportional to the distance between the plates. This means that as the distance between the plates increases, the force on the dielectric decreases.

5. How does the orientation of the dielectric affect the force between parallel plates?

The force on a dielectric is dependent on its orientation between the parallel plates. If the dielectric is aligned parallel to the plates, it will experience a greater force than if it is aligned perpendicular to the plates.

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