Finding electric potential of a sphere with a given volume charge density

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SUMMARY

The discussion focuses on calculating the electric potential \( V \) inside a sphere with a non-uniform volume charge density defined as \( Pe = Po \left(1 - \frac{r^2}{r0^2}\right) \). The user initially derived the enclosed charge \( Q_{encl} \) and the electric field \( E \) but arrived at an incorrect expression for \( V \). The correct approach involves verifying the volume charge density and ensuring proper integration of the electric field to determine the potential accurately.

PREREQUISITES
  • Understanding of electrostatics, specifically electric potential and electric fields.
  • Familiarity with calculus, particularly integration techniques.
  • Knowledge of Gauss's law and its application to spherical charge distributions.
  • Concept of volume charge density and its implications in electric field calculations.
NEXT STEPS
  • Review the derivation of electric potential from electric field using integration techniques.
  • Study Gauss's law and its application to non-uniform charge distributions.
  • Examine examples of electric potential calculations for spherical charge distributions.
  • Learn about the implications of charge density variations on electric field and potential.
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Students studying electromagnetism, physics educators, and anyone involved in solving electrostatics problems related to electric potential and charge distributions.

citra
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Homework Statement


the volume charge density Pe= Po (1- (r^2/r0^2))
the sphere has a radius of r0
and r is measured from the center
for a point P inside the sphere (r<r0), determine the electric potential V if V=0 at infinity

Homework Equations


E= Qencl/ eps0*A= kQ/r^2
Qencl= int(Pe*4pir^2) dr
-int(E)= V

The Attempt at a Solution


first i found Qencl and evaluated it from 0 to r.
Qencl= 4pi*p0 (r^3/ 3 - r^5/5r0^2)
Then E= Po/eps0 ((r/3)- r^3/ 5r0^2)
then the -integral of E= V= p0/eps0 ( (r^2/ 6) - (r^4/20r0^2) - (7r02/60))
but this is the worng answer..any help?
 
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Hi citra, welcome to PF.
You have given volume charge density. But it does not appear correct. Can you check it.
 

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