# Capacitance and distance between plates

## Homework Statement

The question is at
http://dl.getdropbox.com/u/175564/capacitance.JPG [Broken]

## Homework Equations

Q = CV
C = $$\epsilon_{0} A / d$$

## The Attempt at a Solution

The right solution is Q^2 / C that is (h).

I know that C is proportional to the inverse of the distance between plates.
Thus, I suggests that the capacitance should one third of the original value.

The other problem is to have a relation between capacitance and work.
I know W=Fd, where we get a relation to capacitance by d.
This suggests me that the work should one third of the work done with the initial distance between plates in the capacitor.

How would you solve the problem.

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tiny-tim
Homework Helper
Hi soopo!
I know that C is proportional to the inverse of the distance between plates.
Thus, I suggests that the capacitance should one third of the original value.
Yes, that's right!
The other problem is to have a relation between capacitance and work.
I know W=Fd …
You're making it very complicated

work done is energy …

the https://www.physicsforums.com/library.php?do=view_item&itemid=75" getting from one state to another is the difference in energy between them (in a conservative system)

So, although, as you say, work done = ∫force.distance (= ∫charge.voltage), it's much easier to use the standard energy equation for a https://www.physicsforums.com/library.php?do=view_item&itemid=112", which is … ?

Last edited by a moderator:
Hi soopo!

Yes, that's right!

You're making it very complicated

work done is energy …

the https://www.physicsforums.com/library.php?do=view_item&itemid=75" getting from one state to another is the difference in energy between them (in a conservative system)

So, although, as you say, work done = ∫force.distance (= ∫charge.voltage), it's much easier to use the standard energy equation for a https://www.physicsforums.com/library.php?do=view_item&itemid=112", which is … ?
The equation seems to be

W = .5 CV^2

It seems to be obtained by integrating CV with respect to V.
The problem is now to know the upper and lower bounds for the voltage in the integral.
I suggest that the upper one is infinity and the lower one is zero.

If the formula is right, then
V^2 = 2Q / C

However, I cannot see how to get the result.
This suggests me that the equation for the work done in the capacitor is not correct.

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tiny-tim
Homework Helper
Hi soopo!

(try using the X2 tag just above the Reply box )
The equation seems to be

W = .5 CV^2

It seems to be obtained by integrating CV with respect to V.
(whyever are you using W for energy? )

No, it's obtained either by integrating ∫(1/2)QEdx or ∫QVdQ … see the PF Library on https://www.physicsforums.com/library.php?do=view_item&itemid=112"

Anyway, since Q = CV, the energy can also be written .5 Q2/C, which should give you the result almost immediately.

Last edited by a moderator:
Hi soopo!

(try using the X2 tag just above the Reply box )

(whyever are you using W for energy? )

No, it's obtained either by integrating ∫(1/2)QEdx or ∫QVdQ … see the PF Library on https://www.physicsforums.com/library.php?do=view_item&itemid=112"

Anyway, since Q = CV, the energy can also be written .5 Q2/C, which should give you the result almost immediately.