Expression for Electric Field Outside Sphere

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SUMMARY

The discussion focuses on determining the expression for the constant 'a' in the charge density equation ρ = ρ0 - ar² for a uniformly charged sphere of radius R, such that the electric field outside the sphere is zero. The relevant equation for the electric field outside a sphere is E = KQ/r². Participants emphasize the necessity of integrating the charge density over the sphere's volume and applying Gauss's Law to find the total charge required to achieve a zero electric field outside the sphere.

PREREQUISITES
  • Understanding of charge density and its mathematical representation
  • Familiarity with Gauss's Law in electrostatics
  • Knowledge of electric field equations, specifically E = KQ/r²
  • Ability to perform volume integration in calculus
NEXT STEPS
  • Study the application of Gauss's Law in electrostatics
  • Learn about charge density integration techniques
  • Explore the implications of electric fields in different charge distributions
  • Investigate the concept of electric field lines and their behavior around charged objects
USEFUL FOR

Students of physics, particularly those studying electromagnetism, as well as educators and anyone involved in solving problems related to electric fields and charge distributions.

Ryan129
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Homework Statement



The charge desnsity within a uniformly charged sphere of radius R is ρ = ρ0 - ar2, where ρ0 and a are constants and r is the distance from the center. Find an expression for a such that the electric field outside the sphere is zero.

Homework Equations



Electric Field outside a sphere
E = KQ/r2

The Attempt at a Solution



I'm having trouble setting up this problem, I'm not quite sure where to start. If someone could help me I would very much appreciate it.
 
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Ryan129 said:

Homework Statement



The charge desnsity within a uniformly charged sphere of radius R is ρ = ρ0 - ar2, where ρ0 and a are constants and r is the distance from the center. Find an expression for a such that the electric field outside the sphere is zero.

Homework Equations



Electric Field outside a sphere
E = KQ/r2

The Attempt at a Solution



I'm having trouble setting up this problem, I'm not quite sure where to start. If someone could help me I would very much appreciate it.
Hello Ryan129. Welcome to PF !

You will need to integrate the charge density over the whole volume of the sphere & use Gauss's Law to tell you haow muck total charge you need to get that E-field outside of the sphere.

There are other ways to do it.
 

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