Calculating the Electric Potential from an Electric Field problem

[frankfjf]

Homework Statement

A nonconducting sphere has radius R = 2.31cm and uniformly distributed charge q = +3.50 fC. Take the electric potential at the sphere's center to be Vo = 0. What is V at radial distance (a) r = 1.45cm and (b) r = R?

Homework Equations

V = the negative integral from i to f of E * ds

For a, E is kqr/R^3.

For b, E is kq/r^2

The Attempt at a Solution

When I plug all this in I get -5.37 x 10^-4 V and -.001V, respectively. However, when I look at the answer explanation in the student manual, it seems to indicate that ds (or in this case rs) = r/2. Why is it r/2? How is the book getting that for ds? At first I thought ds was equal to r, but I guess I'm not grasping something. Could someone explain why this is so? I basically have the right answer, but only if I divide both my answers by 2.

 

[Pythagorean]

what are your limits of integration and what's your formula for V after you integrate?