Find the electric potential V(r)

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SUMMARY

The discussion focuses on calculating the electric potential V(r) generated by a spherically symmetric charge density defined as ρ = ρ₀ e^(-αr). The user seeks assistance in applying the volume integral of charge density to find V(r) across all space. The solution involves considering the charge as nested spherical shells, which simplifies the integration process by leveraging the symmetry of the problem.

PREREQUISITES
  • Understanding of electric potential and charge density concepts
  • Familiarity with volume integrals in electromagnetism
  • Knowledge of spherical symmetry in electric fields
  • Basic calculus skills for integration
NEXT STEPS
  • Study the derivation of electric potential from charge density using volume integrals
  • Learn about the properties of electric fields generated by spherical charge distributions
  • Explore the concept of nested spherical shells in electrostatics
  • Review examples of calculating electric potential for different charge distributions
USEFUL FOR

Students of electromagnetism, physics educators, and anyone seeking to deepen their understanding of electric potential calculations in electrostatics.

Zamarripa
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Hi, I have a homework of electromagnetism and I got stucked in a problem, can you help me, please?

1. Homework Statement

Find the electric potential V(r) in the space produced by a density charge

(rho) = (rho)0 e-(alpha) r

In spanish:
Enuentra el potencial V(r), en todo el espacio, producido por una densidad de carga:
(rho) = (rho)0 e-(alpha) r

Homework Equations

The Attempt at a Solution


I know that the electric potential produced by a density charge is the volume integral of the density charge by the magnitud of the distance between but I don't know how to take distance in all the space[/B]

 
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Since the charge is spherically symmetric, think of it as nested spherical shells, each with a uniform charge density.
What do you know about the fields generated by such shells?
 

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