Re: Coulomb Force Between A Charge Rod & A Particle
- From: "Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx>
- Date: Thu, 31 Aug 2006 05:21:17 +1000
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?
--
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- From: Adam Teasdale Hartshorne
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- From: Randy Poe
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