Expression for Electric Field Outside Sphere

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SUMMARY

The discussion centers on the application of Gauss's law to determine the electric field outside a uniformly charged sphere. Participants highlight a critical inconsistency in the problem statement, noting that a sphere cannot be both uniformly charged and possess a charge density that varies with radius (r). This contradiction leads to confusion and emphasizes the importance of precise language in physics problems.

PREREQUISITES
  • Understanding of Gauss's law in electrostatics
  • Familiarity with electric field concepts
  • Knowledge of charge density and its implications
  • Basic principles of spherical symmetry in physics
NEXT STEPS
  • Study the derivation of electric fields using Gauss's law
  • Examine examples of charge distributions and their electric fields
  • Learn about the implications of varying charge densities
  • Review common pitfalls in physics problem statements
USEFUL FOR

Students of physics, educators preparing problem sets, and anyone interested in electrostatics and the application of Gauss's law in real-world scenarios.

eric11201120
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Homework Statement
The charge desnsity within a 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.
Relevant Equations
Electric Field outside a sphere
E = KQ/r2
Electric flux
ΦE=∫EdA
I'm not quite sure where to start. If someone could help me I would very much appreciate it.
 
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Hint 1: What does Gauss's law tell you?
Hint 2: Given that expression for charge density, what's the total charge within the sphere?
 
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Steve4Physics said:
But there seems to be a mistake in the question. The sphere can't be both 'uniformly charged' and have a charge density which is a function of r.
Yes, a very sloppily worded question!
 
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