# Potential inside of chrged non-conductive sphere

 P: 328 Potential inside of chrged non-conductive sphere Never mind, I've solved it. You have two different functions for the electric field. If r > R, $$E = \frac{kQ}{r^2}$$ where $$k = \frac{1}{4\pi\epsilon_0}$$ if r < R, $$E = \frac{kQr}{R^3}$$ so V of r < R will be the negative integral of r > R from R to infinity plus the negative integral of r < R from r to R. $$V = - \int^{R}_{\infty} \frac{kQ}{r^2}dr - \int^{r}_{R} \frac{kQr}{R^3}dr$$ $$V = \frac{kR}{R} - \frac{kR}{2R^3}(r^2-R^2) = \frac{2kQR^2}{2R^3} + \frac{kQR^2}{2R^3} - \frac{kQr^2}{2R^3} = \frac{kQ(3R^2 - r^2)}{2R^3}$$ subbing k back in = $$\frac{Q(3R^2 - r^2)}{8 \pi \epsilon_0 R^3}$$ phew.. Hope there are no errors in that haha. I have been up for far too many consecutive hours..