Can Gauss's Law Be Applied to a Charged Circular Ring?

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SUMMARY

Gauss's Law cannot be applied to determine the electric field at point P(0,0,h) due to a uniformly charged circular ring of radius a. The lack of symmetry in the charge distribution prevents the establishment of a uniform electric field over any Gaussian surface. Instead, the solution requires a brute force integration approach to calculate the electric field accurately.

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  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric field concepts and charge distributions
  • Knowledge of integration techniques in physics
  • Basic principles of symmetry in electric fields
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  • Learn about electric field calculations using integration methods
  • Explore examples of electric fields from non-uniform charge distributions
  • Review the principles of symmetry in electrostatics
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Homework Statement


A circular ring of radius a carries a uniform charge q C/m and is placed on x-y plane with axis same as z axis. To determine E at P(0,0,h). My ques is can't we apply gauss theorem? if yes then what will be the gaussian surface? if no then why not?


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The Attempt at a Solution

 
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Gauss's law won't help you because there isn't enough symmetry. Gauss's law helps when you can claim that the field is uniform over a surface--that's not the case here.

You'll have to use brute force and integrate.
 

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