E-Field in a Ring: Homework Solutions

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SUMMARY

The discussion focuses on the electric field (E-field) at the center of a uniformly charged metal ring. It is established that the E-field at the center is zero due to symmetry, as the contributions from opposite sides cancel each other out. Additionally, it is clarified that the E-field is non-zero at other points along the circumference, as the opposing E-fields do not equal in magnitude, leading to a net electric field. This conclusion is critical for understanding the behavior of electric fields in symmetrical charge distributions.

PREREQUISITES
  • Understanding of electric fields and charge distributions
  • Familiarity with symmetry in physics
  • Basic knowledge of vector addition
  • Concept of uniform charge density
NEXT STEPS
  • Study the principles of electric fields in symmetrical charge distributions
  • Explore the concept of superposition in electric fields
  • Learn about Gauss's Law and its applications
  • Investigate the behavior of electric fields in different geometries, such as spheres and cylinders
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Students studying electromagnetism, physics educators, and anyone interested in the mathematical modeling of electric fields in charged systems.

yinx
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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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