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].(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# More Gauss' Law

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