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Could somebody please help me on a problem regarding Potential?

Calculate the potential inside and outside a sphere of radius R and charge Q,in which the charge is distributed uniformly throughout. [Hine: The additive constant for the potential inside the charged sphere must be chose so that the two potentials inside and outside, agree at r=R]

So far, I know that V(outside)=Q/(4*PI*e0*r) when r>R.

How would I find the V(outside) when r<R?

The answer given in the back of the book is V=[Q/(8*PI*e0*R)][3-(r/R)^2]

I have no idea how to obtain it.

Also how would I go about finding the V(inside) for when r>R, and r<R?

Any help would be greatly appreciated!

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# Homework Help: Problem on Potential of Sphere

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