How Do I Calculate Electric Potential at the Location of a Point Charge?

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SUMMARY

The calculation of electric potential at the location of a point charge involves the equation φ(r) = (4πε₀)⁻¹∑[qᵢ |r - r_{qᵢ}|⁻¹] + C. When evaluating the potential at the position of a point charge, the term |r - r_{qᵢ}| approaches zero, leading to a divergence in potential, indicating that the potential is not defined at that specific location. This divergence is a critical aspect of understanding electric potential in electrostatics.

PREREQUISITES
  • Understanding of electrostatics and electric potential
  • Familiarity with the concept of point charges
  • Knowledge of the mathematical representation of electric fields
  • Basic grasp of calculus, particularly limits
NEXT STEPS
  • Study the concept of electric fields generated by point charges
  • Learn about the implications of potential divergence in electrostatics
  • Explore the concept of electric potential energy in relation to point charges
  • Investigate the mathematical treatment of singularities in physics
USEFUL FOR

Students and educators in physics, particularly those focusing on electrostatics, as well as anyone seeking to deepen their understanding of electric potential and its mathematical implications.

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Homework Statement


What should I do when I calculate the potential of point charges at the point of one of the point charges?

Homework Equations


The definition of a potential from point charges are:
[tex]\phi(\textbf{r}) = (4\pi \epsilon_0)^{-1}\sum_{i}[q_i |\textbf{r}-\textbf{r}_{q_i}|^{-1}] + C[/tex]

The Attempt at a Solution


Setting [itex]q_i |\textbf{r}-\textbf{r}_{q_i}|^{-1}=0[/itex] when [itex]\textbf{r}-\textbf{r}_{q_i}=\textbf{0}[/itex]. Haven't seen this anywhere in the lecture material though, but I am guessing that is what one should do. If so, what is the "real" definition of the potential?
 
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The potential diverges as the location of the point charges. It's not defined there.
 

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