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**1. The problem statement, all variables and given/known data**

A non conducting solid sphere with radius [tex] r_1 [/tex] has charge density [tex] \rho_E = \rho_o \frac{r_1}^{r} [/tex]

what is the charge enclosed for [tex] 0 < r < r_1 [/tex] inside the non conducting sphere?

**2. Relevant equations**

[tex] \frac{q_{enc}}^{\frac{4}^{3}} \pi r^3}} = \rho_E = \frac{dq_{enc}}^{4 \pi r^2 dr} [/tex]

(1) [tex] \frac{4}^{3} [/tex] [tex] \pi r^3 \rho_E = q_{enc} [/tex]

[tex] \frac{4}^{3} [/tex] [tex] \pi r^3 \rho_o \frac{r_1}^{r} [/tex] [tex] = \frac{4}^{3} [/tex] [tex]\pi r^2 \rho_o r_1 = q_{enc}[/tex]

[tex] \frac{8}^{3} [/tex] [tex]\pi \rho_o r_1 r dr= dq_{enc}[/tex]

WHY CAN'T I TAKE THIS INTEGRAL TO FIND ENCLOSED CHARGE??????

[tex] \int_{0}^{r} \frac{8}^{3} [/tex] [tex]\pi \rho_o r_1 r dr [/tex] = [tex] \int_{0}^{r} dq_{enc} = Q_{enc} [/tex]

I KNOW I MUST put [tex] \rho_E = \rho_o \frac{r_1}^{r} [/tex] with [tex] dq_{enc} = 4 \pi r^2 dr [/tex] befofe i take the integral, but i'm not sure why (1) does not work.

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