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More Gauss' Law

  1. Feb 2, 2006 #1
    Consider a solid insulating sphere of radius b with nonuniform charge density [tex] \sigma = ar [/tex] where a is a constant. Find the charge Q_r contained within the radius r, when r < b. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to [tex] 4\pi r^2 [/tex].
    I got this part, the answer was Q_r = [tex] \pi ar^4 [/tex].
    The second part says if a = 2 x 10^-6 C/m^4 and b= 1 m, find E at r= 0.6 m. Answer in units of N/C.
    I used the equation [tex] E= Qr/4\pi E_0 R^3 [/tex]
    Plugging in the previous answer for Q gave me [tex] E= (\pi ar^4)r/ 4\pi E_0 R^3 [/tex]
    so [tex] \pi ar^5/4\pi E_0 B^3 [/tex] since R=B in this problem.
    then [tex] \pi (2 x 10^-6)(.6)^5/ 4\pi (8.85 x 10^-12) [/tex]
    This gave me 4378 N/C... which is wrong.
    Help please?
  2. jcsd
  3. Feb 2, 2006 #2
    [tex] E= Qr/4\pi E_0 R^3 [/tex]

    Did you mean Q_r?
  4. Feb 2, 2006 #3
    Yes, sorry I meant Q_r * r.
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