E-Field in a Ring: Homework Solutions

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The E-field at the center of a uniformly charged metal ring is zero due to symmetry, as the electric fields from opposite sides cancel each other out. For points within the circumference of the ring, the E-field is not zero; it varies in magnitude and direction since the contributions from opposite points do not balance out. The confusion arises from the assumption that the E-fields at these points would cancel completely, which they do not. Understanding the vector nature of electric fields is crucial for analyzing points off-center. Clarification on these concepts can enhance comprehension of electric field behavior in symmetrical charge distributions.
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Homework Statement


a) What is the E-field at the center of a metal ring which has uniform charge density?

b) Is E=0 for any other point within the circumference of the ring?2. The attempt at a solution

For (a), since the ring has uniform charge density and is symmetrical, based on symmetry, E-field from opposite sides "cancels" each other out therefore the E field at the center of the ring should be E=0. Am I correct?

For (b), this is the one that got me confused. I was thinking that E-field at all other points (other than the center) should be non-zero as the E-fields from opposite ends at these points are opposite in direction however not equal in magnitude. However I am not too sure about this.

Greatly appreciate if anyone can enlighten me.

-yinx-
 
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