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Old May 5th 2011, 01:41 AM   #1
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Position and velocity vector for the charge in finding retarded potential.

I want to verify that I am correct in setting up the two cases specifically where the charges is moving in a circle radius = a with constant velocity \omega.



Case 1: A point charge q. The position vector w depends on a single variable t_r. The position and velocity vectors are:






Case 2: Charge distribution of line charge density

The position vector depends on both \theta and t. So the position and velocity vectors are:






The reason I claim this is because in the first case, it is a point charge and I don't need \theta. \phi is function of t only.

But in the second case where charge density is function of \theta, the position vector w is function of both t and \theta.

Last edited by yungman; May 5th 2011 at 02:08 AM.
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Old May 5th 2011, 05:22 AM   #2
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Originally Posted by yungman View Post
I want to verify that I am correct in setting up the two cases specifically where the charges is moving in a circle radius = a with constant velocity \omega.



Case 1: A point charge q. The position vector w depends on a single variable t_r. The position and velocity vectors are:






Case 2: Charge distribution of line charge density

The position vector depends on both \theta and t. So the position and velocity vectors are:






The reason I claim this is because in the first case, it is a point charge and I don't need \theta. \phi is function of t only.

But in the second case where charge density is function of \theta, the position vector w is function of both t and \theta.
I'm sorry but I really don't follow what's going on here at all. For case 1 all I can tell you is that you have correctly written the displacement and velocity vectors of an object moving in a circle of radius a about the origin at constant angular speed (omega). For case 2, is the line charge bent into a circle? And we are talking about the motion of what?.

-Dan
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Old May 5th 2011, 10:10 AM   #3
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Originally Posted by topsquark View Post
I'm sorry but I really don't follow what's going on here at all. For case 1 all I can tell you is that you have correctly written the displacement and velocity vectors of an object moving in a circle of radius a about the origin at constant angular speed (omega). For case 2, is the line charge bent into a circle? And we are talking about the motion of what?.

-Dan
Thanks so much for you help.

In case 2, consider the line charge is gluded onto a plastic ring according to the condition given initially. Then the whole ring is spinning at a constant angular velocity \omega.

What I am trying to establish is that for any line charge distributions that spinning in a circle, I have to present the Position vector (which implies the Velocity vector) as function of \phi, which in turn \phi can be function of other independent variables eg.


Case 1 for point charge q spinning at \omega:






Case 2: Charge distribution of GLUDED line charge density spinning at \omega



Last edited by yungman; May 5th 2011 at 10:21 AM.
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Old May 5th 2011, 10:50 AM   #4
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Originally Posted by yungman View Post
Thanks so much for you help.

In case 2, consider the line charge is gluded onto a plastic ring according to the condition given initially. Then the whole ring is spinning at a constant angular velocity \omega.

What I am trying to establish is that for any line charge distributions that spinning in a circle, I have to present the Position vector (which implies the Velocity vector) as function of \phi, which in turn \phi can be function of other independent variables eg.


Case 1 for point charge q spinning at \omega:






Case 2: Charge distribution of GLUDED line charge density spinning at \omega


Okay. Yes for case 1, and basically yes for case 2. I can't see how else to characterize the problem for case 2 any differently than you did. The slight change you might consider is instead of using q for case 2 you might want to use dq. It depends on what further work you are going to do.

-Dan
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Old May 5th 2011, 11:33 AM   #5
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Thanks for you help. The ultimate thing why I am being so particular is because I am looking in terms coordinates transformation specifically from rectangular to cylindrical and visa versa.













Using \phi like this is the only way to make it consistant during coordinates transformations. Please verify I am correct.

Thanks

Alan

Last edited by yungman; May 5th 2011 at 11:35 AM.
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