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Re: There's work, and then there's work



----- Original Message -----
From: "Robert Cohen" <Robert.Cohen@PO-BOX.ESU.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, January 24, 2003 6:15 PM
Subject: Re: There's work, and then there's work


| I'm starting to miss the point in this thread so I'm going to
| butt in and ask some stupid questions again...
|
| Suppose you had two like charges, A and B, of equal charge q
| that are a distance L apart.
|
| Hold charge A still and bring charge B toward
| charge A until the charges are a distance L-x apart.
|
| What was the total work done _on the charges_?

W = (qqk)*(1/(L-x) - 1/L), where k = 1/(4*PI*epsilon)
This is the work done on the charge system both in the mechanical sense of
"work" and in the FLT sense of "work".

|
| When both charges are released at once, the charges separate.
| When they reach a distance L apart, what is the kinetic
| energy of each charge?

W/2 for each charge.

|
| I would think that the kinetic energy equals the total work
| done on the charges but maybe I'm missing something.

Yes, you are not missing anything.

|
| If two people have a different answer for the total work done,
| that seems to mean that they would have different answers for
| the total kinetic energy, which should be easily testable, no?

Yes

|
| If this has nothing to do with the discussion, please
| tell me why.
|
| Thank you for any guidance you can provide in this area.
| ____________________________________________
| Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu=
| /~bbq
| Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301
|
| > -----Original Message-----
| > From: David Rutherford [mailto:drutherford@SOFTCOM.NET]
| > Sent: Thursday, January 23, 2003 8:57 PM
| > To: PHYS-L@lists.nau.edu
| > Subject: Re: There's work, and then there's work
| >=20
| >=20
| > John Mallinckrodt wrote:
| > >
| > > David Rutherford wrote:
| > >
| > > >Answer my first question, first:
| > > >
| > > >"How do you propose to assemble a configuration, in the=20
| > first place, if
| > > >the assembled charges keep flying off every time you bring in a =
| new
| > > >one?"
| > >
| > > I'd hold them so they don't move.
| >=20
| > Why? In the conventional way of calculating the energy of a=20
| > distribution
| > of charges, you don't even consider the field of the particle you a=
| re
| > bringing in, so you don't have to worry about it. In the case of a =
| two
| > particle distribution, the field of the second particle is not even
| > included in the calculation of the energy of the distribution. So b=
| y
| > calculating the energy the conventional way, you get only=20
| > _half_ of the
| > _actual_ energy of the distribution (for two identical particles). =
| Go
| > figure!?#@*
| >=20
| > > >Then please show me how you determined that my result=20
| > predicts that the
| > > >energy stored by a capacitor is CV^2. Show your work.
| > >
| > > Fine. You double count the contribution of each charge to the to=
| tal
| > > energy. Therefore, since the correct answer is 1/2 CV^2, you get
| > > CV^2.
| >=20
| > No. Think of a parallel plate capacitor as two oppositely charged
| > particles flattened into two oppositely charged parallel plates. Us=
| ing
| > the same (conventional) method that was used to find the energy of =
| the
| > two charge distribution, above, you can see that the total=20
| > field of the
| > (assembled) capacitor only includes the field of _one_ of the plate=
| s.
| > That means that, using this method, you get 1/4 CV^2, not 1/2=20
| > CV^2. But
| > using my method, in which the fields of _both_ plates are considere=
| d,
| > you get 1/2 CV^2, which is the _correct_ result.
| >=20
| > I'm assuming that, since you used this example, there is experiment=
| al
| > evidence corroborating this. In that case, the evidence verifies my
| > result for the energy (density) of a charge distribution (and=20
| > a parallel
| > plate capacitor), and proves that the conventional result for=20
| > the energy
| > (density) of a charge distribution is incorrect.
| >=20
| > If you have any other "relevant experimental result[s]" that my the=
| ory
| > "violates", let's see them. It'll be a pleasure to shoot down yet
| > another conventional physics Dodo Bird.