# Potential of a uniformyl charged sphere

1. Apr 2, 2013

### ehabmozart

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

The question asks to find the potential due to a uniformly charged sphere at r<R where R is the radius.

2. Relevant equations

Va-Vb= ∫ E dr from a → b

3. The attempt at a solution

My attempt was like this

Va is to be a the point of interest r.. Vb to be R... We know Vb to be KQ/R... Now E inside the sphere is KQr/R^3 .. After integration with respect to r we get (R^2-r^2)*Kq/2R^3 ... Thus the net potential at Va is Vb + the integral which is KQ/R + (R^2-r^2)*Kq/2R^3 ... However, this isn't the answer given.. Where was my mistake??
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 2, 2013

### Staff: Mentor

How does it differ from the answer given?
Note that it is possible to simplify your expression.

3. Apr 2, 2013

### ehabmozart

I am not able to simplify.. Can you help me?

4. Apr 3, 2013

### Staff: Mentor

Just use (a-b)/c = a/c - b/c for (R^2-r^2)*Kq/(2R^3).