- #1

NeonJay

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## Homework Statement

Positive electric charge Q is distributed uniformly throughout the volume of an insulating sphere with radius R. From the expression for E=kQ/r^2 for r>R and E=kQr/R^3 for r<R, find the expression for the electric potential V as a function of r both inside and outside the uniformly charged sphere. Assume that V = 0 at infinity.

k=1/(4*π*ε

_{0})

## Homework Equations

[tex]\int_A^B\vec{E}\cdot\mathrm{d}\vec{r} = V(A) - V(B)[/tex]

**2.5. Apparent Answer**

(kQ/2R)[3-(r^2)/(R^2)]

Apologies ... I'm not very knowledgeable in tex, but that last part would read r-squared over R-squared.

## The Attempt at a Solution

I have already obtained V = kQ/r for r>R. This was a simple antiderivative.

I'm getting really caught up on r<R. I've tried integrating from 0 to r, 0 to R, r to R, and backwards versions of the same. Nothing comes to the answer in 2.5 above. I'm really at a loss for how this integral should be done. I can understand most of it except for the 3 in the second expression; where the heck does it come from? I've seen this answer in a couple of different places, but none of them actually explain it.

Any help would be appreciated. Thanks ahead of time.