# Potential inside of chrged non-conductive sphere

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 P: 11 1. The problem statement, all variables and given/known data A charge is distributed uniformly throughout a non-conducting spherical volume of radius R. Show, that the potential at distance r from center (r
 P: 11 I made a small mistake in typing the formula on V that I obtained. It should be: V(r)=-q*r^2/(8*PI*e0*R^3)
 P: 328 And R = radius of gaussian surface r = radius of your sphere? please be precise.
 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..
 P: 11 Thank you very much for the reply! I have just one more question: why should I integrate from infinity to zero, not from zero to infinity?
 P: 11 Sorry again: from inf to r not from r to inf, I meant.
 P: 11 One more correction: Why should I integrate from infinity to r not from zero to r? I hope, now it's ok...
 P: 328 because if we integrated from zero to r, that would give us V for inside the gaussian surface aswell as inside the sphere. Sorry for the late reply I was away for sometime.

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