Concentric rings and net electric fields

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SUMMARY

The discussion centers on calculating the charge required on a larger concentric ring to achieve a net electric field of zero at point P, located on the z-axis. The smaller ring has a uniformly distributed charge of +Q, while the larger ring, with a radius of R' = 3.00R, must have a negative charge to counterbalance the electric field produced by the smaller ring. The relevant equation used is E = kqz / (z² + R²)^(3/2). The final calculated charge for the larger ring is -13/5 Q, confirming the necessity of a negative charge to achieve equilibrium.

PREREQUISITES
  • Understanding of electric fields generated by charged rings
  • Familiarity with the equation E = kqz / (z² + R²)^(3/2)
  • Knowledge of charge distribution and its effects on electric fields
  • Basic algebra for solving equations
NEXT STEPS
  • Study the principles of electric fields from charged objects
  • Learn about superposition of electric fields in multiple charge systems
  • Explore the concept of electric field lines and their implications
  • Investigate the effects of varying charge distributions on electric fields
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone involved in solving problems related to electric fields and charge distributions.

MasterWu77
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Homework Statement



The figure below shows two concentric rings, of radii R and R ' = 3.00R, that lie on the same plane. Point P lies on the central z axis, at distance D = 2.00R from the center of the rings. The smaller ring has uniformly distributed charge +Q. What must be the uniformly distributed charge on the larger ring if the net electric field at point P due to the two rings is to be zero?

_____ x Q

<a href="[PLAIN]http://s323.photobucket.com/albums/nn457/MasterWu77/?action=view&current=physics.gif" target="_blank"><img src="http://i323.photobucket.com/albums/nn457/MasterWu77/physics.gif" border="0" alt="physics homework"></a>[/PLAIN]

Homework Equations



E= kqz/ (z^2+R^2)^(3/2)

The Attempt at a Solution



This is my first time here on this site so please bear with me as I'm not too sure how to work things haha. I'm unsure of whether the image i posted will show up or not. but it is basically 2 concentric rings, one small one (R) inside of a bigger one (R') with the radi as described. There is a line (z-axis) with the point P on it that is a distance D away from the rings. The first time I tried the problem I used the wrong formula and missed the question twice. But the last time I tried the problem, I used the equation describes the electrical field of a charged ring. I set that equation for each one of the rings and then set the equations equal to each other since the net electric field is zero. I then solved for the charge compared to the charge of the unknown (larger ring). The last answer I came up with was 13/5. And I set that number negative, because the smaller ring was a positive number so the bigger ring would have to be a negative number to make the net electric field at P = 0.

I feel like I might just missing a small little fact or maybe I'm not thinking about the end correctly. Again, this is my first time so please let me know if I'm doing anything wrong. I have also entered an answer in 3 times and I'm getting scared that I'm running out of tries.

Thanks for your time!
 
Last edited by a moderator:
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Hi MasterWu77,
Welcome to PF.
To check your result, show your calculations. Your approach is correct.
 
hi sorry it took me so long to respond. but i looked at the problem and realized my mistake, thanks for your help!
 

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