Work required to move capacitor plates

[Frostfire]

Homework Statement

Determine the work required to move the plates of an ideal parallel plate capacitor from a separation distance of D to an integer multiple of D, (assume only one moves for simplicity). The each plate has an area A.

Homework Equations

F = q^2 /( 2 e_0 A) field strength between the plates
$$\Delta$$ V = U/q
$$\Delta$$U = -W
$$\Delta$$V= Qd/e_0 A

The Attempt at a Solution

moving the terms above around I came up with U = Qdq/e_0A
I know I need an integral here, probably evaluated between D and multiple of D(its a general solution that's needed)
Am I on the right track?

 

[xcvxcvvc]

Though it's a little cheap and probably not what your professor had in mind, you can use the equation for energy density(J/m^2) stored in an electric field to solve this problem. Do final energy stored minus initial energy stored to calculate what energy was added (or done) to the system.

 

[Frostfire]

I appreciate the reply. I thought about that, but I use that in another part of the problem, not that I can't use it again since its different variables, but I am fairly certain I'll be graded on the diversity of methods used.

Anyone know if that integral approach would work or am I grasping at fog?

 

[Dadface]

Why not use the appropriate equation for energy stored in a capacitor?

 

[matt_crouch]

well since you know the force between the two plates

Work is

W=Integral (Fdr)

 

[Frostfire]

Thats what I thought but I encounter a problem, when I compare the integral result to one obtained by use of potential energy, I am getting a different result depending on different terms. Considering that the work should be the same, I am stuck. Is there anyway Q^2= Vbat?

 

[Dadface]

In the question has the capacitor been charged and disconnected from the battery?If so Q remains constant and V changes if the plate separation is changed.If the capacitor remains connected to the battery V remains constant and Q changes.

 

[lolrelativity]

Also remember the potential energy of a system is (CV^2)/2