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

AI Thread Summary
Gauss's Law cannot be applied to a charged circular ring due to the lack of symmetry in the electric field around the ring. The field at point P(0,0,h) does not exhibit uniformity, which is a requirement for using Gauss's theorem effectively. As a result, the solution requires a more complex approach involving integration to determine the electric field. The discussion emphasizes the necessity of understanding the conditions under which Gauss's Law is applicable. Ultimately, the problem necessitates a detailed calculation rather than a straightforward application of Gauss's Law.
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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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