| Topic: |
Science > Physics |
| User: |
"Adam Teasdale Hartshorne" |
| Date: |
30 Aug 2006 12:33:41 PM |
| Object: |
Coulomb Force Between A Charge Rod & A Particle |
Hi All,
I have a simple physics question, which I wonder if somebody could help
me with as I am a computer science person trying to use Coulomb force as
an error metric.
In 3D space, if I have a charged rod, (length l with start and end
points, r1 and r2) and an oppositely charged particle positined at p1,
what is the coulomb force between them?
I am assuming you have to integrate the standard coulomb force between
two particles along the rod (Excuse the poor english),
Any help is much appreciated,
Adam
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| User: "Randy Poe" |
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| Title: Re: Coulomb Force Between A Charge Rod & A Particle |
30 Aug 2006 01:10:22 PM |
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Adam Teasdale Hartshorne wrote:
Hi All,
I have a simple physics question, which I wonder if somebody could help
me with as I am a computer science person trying to use Coulomb force as
an error metric.
In 3D space, if I have a charged rod, (length l with start and end
points, r1 and r2) and an oppositely charged particle positined at p1,
what is the coulomb force between them?
I am assuming you have to integrate the standard coulomb force between
two particles along the rod (Excuse the poor english),
That is correct. However, it isn't a very difficult integral.
See here:
http://www.phys.uri.edu/~gerhard/PHY204/tsl31.pdf
I think you will find "Electric Field of Charged Rod (2)" most
useful. There are expressions for the x and y components
of the vector electric field. The force on the particle at p1 is
E times the charge at p1.
- Randy
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| User: "Adam Teasdale Hartshorne" |
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| Title: Re: Coulomb Force Between A Charge Rod & A Particle |
30 Aug 2006 01:14:52 PM |
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Randy Poe wrote:
Adam Teasdale Hartshorne wrote:
Hi All,
I have a simple physics question, which I wonder if somebody could help
me with as I am a computer science person trying to use Coulomb force as
an error metric.
In 3D space, if I have a charged rod, (length l with start and end
points, r1 and r2) and an oppositely charged particle positined at p1,
what is the coulomb force between them?
I am assuming you have to integrate the standard coulomb force between
two particles along the rod (Excuse the poor english),
That is correct. However, it isn't a very difficult integral.
See here:
http://www.phys.uri.edu/~gerhard/PHY204/tsl31.pdf
I think you will find "Electric Field of Charged Rod (2)" most
useful. There are expressions for the x and y components
of the vector electric field. The force on the particle at p1 is
E times the charge at p1.
- Randy
What about in 3d?
Adam
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| User: "Timo A. Nieminen" |
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| Title: Re: Coulomb Force Between A Charge Rod & A Particle |
30 Aug 2006 02:21:17 PM |
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On Wed, 30 Aug 2006, Adam Teasdale Hartshorne wrote:
Randy Poe wrote:
Adam Teasdale Hartshorne wrote:
I have a simple physics question, which I wonder if somebody could help
me with as I am a computer science person trying to use Coulomb force as
an error metric.
In 3D space, if I have a charged rod, (length l with start and end
points, r1 and r2) and an oppositely charged particle positined at p1,
what is the coulomb force between them?
I am assuming you have to integrate the standard coulomb force between
two particles along the rod (Excuse the poor english),
That is correct. However, it isn't a very difficult integral.
See here:
http://www.phys.uri.edu/~gerhard/PHY204/tsl31.pdf
I think you will find "Electric Field of Charged Rod (2)" most
useful. There are expressions for the x and y components
of the vector electric field. The force on the particle at p1 is
E times the charge at p1.
What about in 3d?
It's effectively a 2D problem. What is the "most natural" coordinate
system to use? How about cylindrical coordinates with the rod on the
z-axis, at the origin? The x and y components above are then the r and z
components, and you have the full 3D solution, straight from the 2D
simplification. If you want to use a less convenient coordinate system,
just transform coordinates and E field vectors as needed (wherein one
might find a nice lesson in the difference between coordinates and vector
components!).
Exercise: why is the phi component zero?
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "" |
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| Title: Re: Coulomb Force Between A Charge Rod & A Particle |
30 Aug 2006 02:21:03 PM |
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In article <ed4i5l$pcb$2@mail.dcs.warwick.ac.uk>, Adam Teasdale Hartshorne <adam@dcs.warwick.ac.uk> writes:
Hi All,
I have a simple physics question, which I wonder if somebody could help
me with as I am a computer science person trying to use Coulomb force as
an error metric.
In 3D space, if I have a charged rod, (length l with start and end
points, r1 and r2) and an oppositely charged particle positined at p1,
what is the coulomb force between them?
I am assuming you have to integrate the standard coulomb force between
two particles along the rod (Excuse the poor english),
Yes, that's just what you have to do. Note that there are two
possible cases here:
1) The rod is non conductive and the charge distribution along it is
given (in the simplest case it is a uniform distribution). In this
case plain integration will do.
2) The rod is conductive. In this case, whatever charge is present
on it will redistribute itself due to the presence of the external
charge, so as to keep the rod an equipotential. So, you've a coupled
problem of finding the distribution and the forces. Much more
complicated.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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