Work to Move parallel capacitor Plates

In summary: I'm not sure what you mean. You are calculating the work done on both plates--it's the same on both so that's why you multiply by 2.But since the two plates experience the same force and movement, why not take advantage of symmetry?Thanks!
  • #1
Typhon4ever
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0
Hi, in my book there are two capacitor plates distance x apart (they are kept connected to a constant voltage source). These plates are moved apart to distance 3x. In order to find the work done to move the capacitors apart (using W=F dl=QE dl), my book takes the charge Q of one plate and electric field felt on that one plate and integrates it from x to 3x. Why can't we take the take the charge and electric field felt on both plates and integrate half the distance of x to 3x?
 
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  • #2
Typhon4ever said:
In order to find the work done to move the capacitors apart (using W=F dl=QE dl), my book takes the charge Q of one plate and electric field felt on that one plate and integrates it from x to 3x.
OK, but Q and E are not constant as the distance changes.

Why can't we take the take the charge and electric field felt on both plates and integrate half the distance of x to 3x?
Who says you can't?
 
  • #3
Doc Al said:
OK, but Q and E are not constant as the distance changes.


Who says you can't?

Okay, how would I set up the integration of both plates? My book says the Q on one plate is [itex]\frac{\epsilon_0 A V}{L}[/itex] and the electric field felt on that one plate is [itex]\frac{V}{2L}[/itex] how would I change these to be both plates?
 
  • #4
Typhon4ever said:
Okay, how would I set up the integration of both plates? My book says the Q on one plate is [itex]\frac{\epsilon_0 A V}{L}[/itex] and the electric field felt on that one plate is [itex]\frac{V}{2L}[/itex] how would I change these to be both plates?
The only thing that would change would be your variable of integration. Since you want to move each plate half the distance, for each plate the position y would relate to the distance between them by L = 2y. Then just integrate from y = x/2 to y = 3x/2. You'll need to multiply your answer by 2, of course.

Compare that to just moving one plate (like in your book). In that case y would be the total distance, so L = y. And you'd integrate from y = x to y = 3x. (And not multiply by 2.)

Each method should give the same answer for the work done.
 
  • #5
Doc Al said:
The only thing that would change would be your variable of integration. Since you want to move each plate half the distance, for each plate the position y would relate to the distance between them by L = 2y. Then just integrate from y = x/2 to y = 3x/2. You'll need to multiply your answer by 2, of course.

Compare that to just moving one plate (like in your book). In that case y would be the total distance, so L = y. And you'd integrate from y = x to y = 3x. (And not multiply by 2.)

Each method should give the same answer for the work done.

Oh, I see. You have to focus on one plate. There is no possible way to calculate work done on both plates at once? Is that because the Q between them both is 0?
 
  • #6
Typhon4ever said:
Oh, I see. You have to focus on one plate. There is no possible way to calculate work done on both plates at once?
I'm not sure what you mean. You are calculating the work done on both plates--it's the same on both so that's why you multiply by 2.
 
  • #7
Doc Al said:
I'm not sure what you mean. You are calculating the work done on both plates--it's the same on both so that's why you multiply by 2.

What I meant is that is there a way to calculate the total work done without multiplying by two? Or can we only calculate the work on one plate and have to double it.
 
  • #8
Typhon4ever said:
What I meant is that is there a way to calculate the total work done without multiplying by two? Or can we only calculate the work on one plate and have to double it.
Well, you can always do the integration twice! Once for each side.
 
  • #9
Doc Al said:
Well, you can always do the integration twice! Once for each side.

Isn't that the same thing as multiplying by 2?
 
  • #10
Typhon4ever said:
Isn't that the same thing as multiplying by 2?
Yep. :wink:

But since the two plates experience the same force and movement, why not take advantage of symmetry?
 
  • #11
Thanks!
 

1. What is the purpose of moving parallel capacitor plates in a circuit?

The purpose of moving parallel capacitor plates is to change the capacitance of the capacitor, which affects the amount of charge it can hold and the potential difference across it. This can be used to control the flow of current in a circuit.

2. How do you move parallel capacitor plates in a circuit?

Parallel capacitor plates can be moved by changing the distance between them, which changes the electric field and affects the capacitance. Alternatively, they can also be moved by changing the surface area of the plates, which also changes the capacitance.

3. What factors affect the movement of parallel capacitor plates?

The movement of parallel capacitor plates is affected by the distance between the plates, the surface area of the plates, the material of the plates, and the dielectric material between the plates. These factors all contribute to the overall capacitance of the capacitor.

4. How does moving parallel capacitor plates affect the electric field?

Moving parallel capacitor plates changes the electric field between the plates, which in turn changes the capacitance. As the plates are moved closer together, the electric field becomes stronger, and as they are moved farther apart, the electric field becomes weaker.

5. What are some practical applications of moving parallel capacitor plates?

Moving parallel capacitor plates can be used in various electronic devices, such as radio tuners, variable capacitors, and touchscreens. They can also be used in circuit design to control the flow of current and adjust the potential difference across different components.

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