Ask Question
30 September, 14:55

A solid uniformly charged insulating sphere has uniform volume charge density p and radius R. Apply Gauss's law to determine an expression for the magnitude of the electric field at an arbitrary distance r from the center of the sphere, such that r < R, in terms of rho and r

+1
Answers (1)
  1. 30 September, 16:49
    0
    electric field E = (1 / 3 e₀) ρ r

    Explanation:

    For the application of the law of Gauss we must build a surface with a simple symmetry, in this case we build a spherical surface within the charged sphere and analyze the amount of charge by this surface.

    The charge within our surface is

    ρ = Q / V

    Q ' = ρ V '

    The volume of the sphere is V = 4/3 π r³

    Q ' = ρ 4/3 π r³

    The symmetry of the sphere gives us which field is perpendicular to the surface, so the integral is reduced to the value of the electric field by the area

    I E da = Q ' / ε₀

    E A = E 4 πi r² = Q ' / ε₀

    E = (1/4 π ε₀) Q ' / r²

    Now you relate the fraction of load Q 'with the total load, for this we use that the density is constant

    R = Q ' / V' = Q / V

    How you want the solution depending on the density (ρ) and the inner radius (r)

    Q ' = R V'

    Q ' = ρ 4/3 π r³

    E = (1 / 4π ε₀) (1 / r²) ρ 4/3 π r³

    E = (1 / 3 e₀) ρ r
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A solid uniformly charged insulating sphere has uniform volume charge density p and radius R. Apply Gauss's law to determine an expression ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers