- #1
Punchlinegirl
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Consider a solid insulating sphere of radius b with nonuniform charge density \sigma = ar 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 4\pi r^2.
I got this part, the answer was Q_r = \pi ar^4.
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 E= Qr/4\pi E_0 R^3
Plugging in the previous answer for Q gave me E= (\pi ar^4)r/ 4\pi E_0 R^3
so \pi ar^5/4\pi E_0 B^3 since R=B in this problem.
then \pi (2 x 10^-6)(.6)^5/ 4\pi (8.85 x 10^-12)
This gave me 4378 N/C... which is wrong.
Help please?
I got this part, the answer was Q_r = \pi ar^4.
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 E= Qr/4\pi E_0 R^3
Plugging in the previous answer for Q gave me E= (\pi ar^4)r/ 4\pi E_0 R^3
so \pi ar^5/4\pi E_0 B^3 since R=B in this problem.
then \pi (2 x 10^-6)(.6)^5/ 4\pi (8.85 x 10^-12)
This gave me 4378 N/C... which is wrong.
Help please?