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Homework Help: Electric Field of a Charged Sphere?

  1. Jul 25, 2017 #1
    1. The problem statement, all variables and given/known data
    A sphere of radius R has total charge Q. The volume charge density (C/m^3) within the sphere is ρ = ρ_0 (1 - r/R).

    This charge density decreases linearly from ρ_0 at the center to zero at the edge of sphere.

    a. Show that ρ_0 = 3Q/πR^3.
    b. Show that the electric field inside the sphere points radially outward with magnitude E = (Qr/4πε_0 R^3) (4 - 3 r/R).
    c. Find the electric field outside the sphere (r > R).

    2. Relevant equations
    Volume of a Sphere: V = 4/3 πR^3.

    3. The attempt at a solution
    I knew that ρ = Q/V and could make this equal to our given value of ρ to find ρ_0, but I was unable to get rid of the 4 in the denominator to find ρ_0.
  2. jcsd
  3. Jul 25, 2017 #2


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    This is incorrect. The sphere does not have uniform charge. You need to integrate the charge density to relate it to the total charge.
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