Why Can't the Potential Integral Formula Be Used for Infinite Line Charges?

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SUMMARY

The potential integral formula cannot be applied to infinite uniform line charges due to the divergence of the potential at infinite distances. Specifically, for a line charge density ρlo located on the z-axis, the potential integral assumes finite charge distributions, leading to undefined results when extended to infinity. This limitation is rooted in the mathematical properties of the potential integral, which relies on the convergence of the integral over the charge distribution.

PREREQUISITES
  • Understanding of electrostatics and electric potential
  • Familiarity with line charge density concepts
  • Knowledge of calculus, particularly integration techniques
  • Basic principles of divergence and convergence in mathematical analysis
NEXT STEPS
  • Study the mathematical derivation of the potential integral for finite charge distributions
  • Explore the concept of divergence in electric fields and potentials
  • Learn about alternative methods for calculating potentials from infinite charge distributions
  • Investigate the implications of charge distribution on electric field behavior
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Physics students, electrical engineers, and researchers in electromagnetism seeking to deepen their understanding of electric potential calculations involving infinite charge distributions.

brad sue
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Hi ,
i have a question I don't know how to answer:

Explain why the potential integral formula cannot be used to directly determine the potential from an infinite uniform line charge ρlo that is on the z axis.

When we talk about it in class, I learn that the potential integral was used for finite displacement. I d read the textbook but I did not have other information.

So I there other reason to answer this question?

B.
 
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